@vit.ac.in

Professor(Higher Academic Grade)

Vellore Institute of Technology (VIT)

PHD (Mathematics) 1995, UNIVERSITY OF MADRAS Madras Christian College: Chennai, 600059; TN, INDIA

M.Phil (Mathematics) 1990 UNIVERSITY OF MADRAS Madras Christian College(Autonomous): Chennai, 600059; TN, INDIA

M.Sc (Mathematics)-1989 UNIVERSITY OF MADRAS Loyola College(Autonomous): Chennai, 600034 TN, INDIA

B.Sc (Mathematics)-1987 UNIVERSITY OF MADRAS Sacred Heart College: Tirupattur, TN, INDIA

Complex Analysis-Geometric Function Theory

218

Scopus Publications

3528

Scholar Citations

30

Scholar h-index

87

Scholar i10-index

- Ozaki-Type Bi-Close-to-Convex and Bi-Concave Functions Involving a Modified Caputo’s Fractional Operator Linked with a Three-Leaf Function

Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Daniel Breaz, Georgia Irina Oros, and Sheza M. El-Deeb

MDPI AG

The focus of the present work is on the establishment and investigation of the coefficient estimates of two new subclasses of bi-close-to-convex functions and bi-concave functions; these are of an Ozaki type and involve a modified Caputo’s fractional operator that is associated with three-leaf functions in the open unit disc. The classes are defined using the notion of subordination based on the previously established fractional integral operators and classes of starlike functions associated with a three-leaf function. For functions in these classes, the Fekete-Szegö inequalities and the initial coefficients, |a2| and |a3|, are discussed. Several new implications of the findings are also highlighted as corollaries. - Starlike Functions of the Miller–Ross-Type Poisson Distribution in the Janowski Domain

Gangadharan Murugusundaramoorthy, Hatun Özlem Güney, and Daniel Breaz

MDPI AG

In this paper, considering the various important applications of Miller–Ross functions in the fields of applied sciences, we introduced a new class of analytic functions f, utilizing the concept of Miller–Ross functions in the region of the Janowski domain. Furthermore, we obtained initial coefficients of Taylor series expansion of f, coefficient inequalities for f−1 and the Fekete–Szegö problem. We also covered some key geometric properties for functions f in this newly formed class, such as the necessary and sufficient condition, convex combination, sequential subordination and partial sum findings. - Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

Kadhavoor R. Karthikeyan and Gangadharan Murugusundaramoorthy

MDPI AG

Motivated by the notion of multiplicative calculus, more precisely multiplicative derivatives, we used the concept of subordination to create a new class of starlike functions. Because we attempted to operate within the existing framework of the design of analytic functions, a number of restrictions, which are in fact strong constraints, have been placed. We redefined our new class of functions using the three-parameter Mittag–Leffler function (Srivastava–Tomovski generalization of the Mittag–Leffler function), in order to increase the study’s adaptability. Coefficient estimates and their Fekete-Szegő inequalities are our main results. We have included a couple of examples to show the closure and inclusion properties of our defined class. Further, interesting bounds of logarithmic coefficients and their corresponding Fekete–Szegő functionals have also been obtained. - A class of ϑ -bi-pseudo-starlike functions with respect to symmetric points associated with Telephone numbers

G. Murugusundaramoorthy, N. E. Cho, and K. Vijaya

Springer Science and Business Media LLC - Coefficient bounds for certain families of bi-Bazilevič and bi-Ozaki-close-to-convex functions

Muajebah Hidan, Abbas Kareem Wanas, Faiz Chaseb Khudher, Gangadharan Murugusundaramoorthy, and Mohamed Abdalla

American Institute of Mathematical Sciences (AIMS)

<abstract><p>The aim of this work is to introduce two families, $ \\mathcal{B}_{\\Sigma}(\\wp; \\vartheta) $ and $ \\mathcal{O}_{\\Sigma}(\\varkappa; \\vartheta) $, of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings.</p></abstract> - On λ-pseudo bi-starlike functions related with Fibonacci numbers

Kaliyappan Vijaya, Gangadharan Murugusundaramoorthy, and Hatun Özlem Güney

Centre pour la Communication Scientifique Directe (CCSD)

In this paper we define a new subclass $\\lambda$-bi-pseudo-starlike functions of $\\Sigma$ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for $f\\in\\mathcal{PSL}_{\\Sigma}^\\lambda(\\tilde{p}(z)).$ Further we determine the Fekete-Szeg\\"{o} result for the function class $\\mathcal{PSL}_{\\Sigma}^\\lambda(\\tilde{p}(z))$ and for special cases, corollaries are stated which some of them are new and have not been studied so far. - Binomial Series-Confluent Hypergeometric Distribution and Its Applications on Subclasses of Multivalent Functions

Ibtisam Aldawish, Sheza M. El-Deeb, and Gangadharan Murugusundaramoorthy

MDPI AG

Over the past ten years, analytical functions’ reputation in the literature and their application have grown. We study some practical issues pertaining to multivalent functions with bounded boundary rotation that associate with the combination of confluent hypergeometric functions and binomial series in this research. A novel subset of multivalent functions is established through the use of convolution products and specific inclusion properties are examined through the application of second order differential inequalities in the complex plane. Furthermore, for multivalent functions, we examined inclusion findings using Bernardi integral operators. Moreover, we will demonstrate how the class proposed in this study, in conjunction with the acquired results, generalizes other well-known (or recently discovered) works that are called out as exceptions in the literature. - Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator

Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, Daniel Breaz, and Luminiţa-Ioana Cotîrlǎ

MDPI AG

In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects such as coefficient bounds, convolution conservation, and convexity constraints. Next, using sufficiency criteria, we calculate the sharp bounds of the real parts of the ratios of harmonic functions to their sequences of partial sums. In addition, for the first time some of the interesting implications of the q-Srivastava–Attiya operator in harmonic functions are also included. - Φ–LIKE ANALYTIC FUNCTIONS ASSOCIATED WITH A VERTICAL DOMAIN

Serkan Araci, K. R. Karthikeyan, G. Murugusundaramoorthy, and Bilal Khan

Element d.o.o. - Initial Coefficients and Fekete-Szego Inequalities for Functions Related to van der Pol Numbers (VPN)

Gangadharan Murugusundaramoorthy and Teodor Bulboacă

Walter de Gruyter GmbH

ABSTRACT The purpose of this paper is to find coefficient estimates for the class of functions ℳ N ( γ , ϑ , λ ) consisting of analytic functions f normalized by f(0) = f′(0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a 2, a 3, and the Fekete-Szegő functional upper bound for f ∈ ℳ N ( γ , ϑ , λ ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series. - Harmonic functions associated with Pascal distribution series

B.A. Frasin, M.O. Oluwayemi, S. Porwal, and G. Murugusundaramoorthy

Elsevier BV - On λ-pseudo starlike functions associated with vertical strip domain

Janusz Sokół, G. Murugusundaramoorthy, and K. Vijaya

World Scientific Pub Co Pte Ltd

We consider the class of [Formula: see text]-pseudo starlike functions [Formula: see text] such that [Formula: see text] maps the open unit disk [Formula: see text] onto a strip domain [Formula: see text] with [Formula: see text] for some [Formula: see text], [Formula: see text]. We estimate [Formula: see text], [Formula: see text] and solve the Fekete–Szegö problem for functions in this class. - Certain Class of Bi-Univalent Functions Defined by Sălăgean q-Difference Operator Related with Involution Numbers

Daniel Breaz, Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, and Luminiţa-Ioana Cotîrlǎ

MDPI AG

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers. - Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients

Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, and Teodor Bulboacă

MDPI AG

In this article we introduce three new subclasses of the class of bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates a2 and a3 of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions. - Sakaguchi Type Starlike Functions Related with Miller-Ross-Type Poisson Distribution in Janowski Domain

Sheza M. El-Deeb, Asma Alharbi, and Gangadharan Murugusundaramoorthy

MDPI AG

In this research, using the Poisson-type Miller-Ross distribution, we introduce new subclasses Sakaguchi type of star functions with respect to symmetric and conjugate points and discusses their characteristic properties and coefficient estimates. Furthermore, we proved that the class is closed by an integral transformation. In addition, we pointed out some new subclasses and listed their geometric properties according to specializing in parameters that are new and no longer studied in conjunction with a Miller-Ross Poisson distribution. - On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli

Lech Gruszecki, Adam Lecko, Gangadharan Murugusundaramoorthy, and Srikandan Sivasubramanian

MDPI AG

In this paper, we introduce and study the class of analytic functions in the unit disc, which are derived from Robertson’s analytic formula for starlike functions with respect to a boundary point combined with a subordination involving lemniscate of Bernoulli and crescent shaped domains. Using their symmetry property, the basic geometrical and analytical properties of the introduced classes were proved. Early coefficients and the Fekete–Szegö functional were estimated. Results for both classes were also obtained by applying the theory of differential subordinations. - Pascu-Rønning Type Meromorphic Functions Based on Sălăgean-Erdély–Kober Operator

Sheza M. El-Deeb, Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, and Alhanouf Alburaikan

MDPI AG

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ*:={ϑ∈C:0<|ϑ|<1} by making use of the Erdély–Kober operator Iς,ϱτ,κ which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far. - Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers

Kaliappan Vijaya and Gangadharan Murugusundaramoorthy

MDPI AG

For the first time, we attempted to define two new sub-classes of bi-univalent functions in the open unit disc of the complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients of functions in these classes were obtained. Moreover, we also determined the Fekete–Szegö inequalities for function in these and several related corollaries. - Certain subclasses of λ -pseudo bi-univalent functions with respect to symmetric points associated with the Gegenbauer polynomial

Adnan Ghazy Al Amoush and Gangadharan Murugusundaramoorthy

Springer Science and Business Media LLC - Spiral-like functions associated with Miller–Ross-type Poisson distribution series

Sevtap Sümer Eker, Gangadharan Murugusundaramoorthy, Bilal Şeker, and Bilal Çekiç

Springer Science and Business Media LLC - Starlike Functions Based on Ruscheweyh q−Differential Operator defined in Janowski Domain

Luminiţa-Ioana Cotîrlǎ and Gangadharan Murugusundaramoorthy

MDPI AG

In this paper, we make use of the concept of q−calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of Janowski type starlike functions and to find the Fekete–Szegö functional. A similar results have been done for the function ℘−1. Further, for functions in newly defined class we determine coefficient estimates, distortion bounds, radius problems, results related to partial sums. - ON JANOWSKI TYPE HARMONIC FUNCTIONS ASSOCIATED WITH THE WRIGHT HYPERGEOMETRIC FUNCTIONS

G. Murugusundaramoorthy and S. Porwal

Vladikavkaz Scientific Centre of the Russian Academy of Sciences

In our present study we consider Janowski type harmonic functions class introduced and studied by Dziok, whose members are given by $h(z) = z + \\sum_{n=2}^{\\infty} h_n z^n$ and $g(z) = \\sum_{n=1}^{\\infty} g_n z^n$, such that $\\mathcal{ST}_{H}(F,G)=\\big\\{ f = h + \\bar{g} \\in {H}:\\frac{\\mathfrak{D}_H f(z)}{f(z)}\\prec\\frac{1+Fz}{1+G z};\\, (-G \\leq F < G \\leq 1, \\text{ with } g_1=0)\\big\\},$ where $\\mathfrak{D}_H f(z) = zh'(z)-\\overline{zg'(z)}\\,$ and $z\\in \\mathbb{U}=\\{z:z\\in \\mathbb{C} \\text{ and }|z| < 1 \\}.$ We investigate an~association between these subclasses of harmonic univalent functions by applying certain convolution operator concerning Wright's generalized hypergeometric functions and several special cases are given as a corollary. Moreover we pointed out certain connections between Janowski-type harmonic functions class involving the generalized Mittag–Leffler functions. Relevant connections of the results presented herewith various well-known results are briefly indicated. - COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH THE GEGENBAUER POLYNOMIAL

- Ozaki-Type Bi-Close-to-Convex and Bi-Concave Functions Involving a Modified Caputo’s Fractional Operator Linked with a Three-Leaf Function

K Vijaya, G Murugusundaramoorthy, D Breaz, GI Oros, SM El-Deeb

Fractal and Fractional 8 (4), 220 2024 - Starlike Functions of the Miller–Ross-Type Poisson Distribution in the Janowski Domain

G Murugusundaramoorthy, H Gney, D Breaz

Mathematics 12 (6), 795 2024 - A class of -bi-pseudo-starlike functions with respect to symmetric points associated with Telephone numbers

G Murugusundaramoorthy, NE Cho, K Vijaya

Afrika Matematika 35 (1), 17 2024 - Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

KR Karthikeyan, G Murugusundaramoorthy

Fractal and Fractional 8 (3), 131 2024 - Sufficient conditions of subclasses of spiral-like functions associated with Mittag-Leffler functions

G Murugusundaramoorthy, T Bulboacă

Kragujevac Journal of Mathematics 48 (6), 921-934 2024 - Binomial Series-Confluent Hypergeometric Distribution and Its Applications on Subclasses of Multivalent Functions

I Aldawish, SM El-Deeb, G Murugusundaramoorthy

Symmetry 15 (12), 2186 2023 - Subclasses of Noshiro-Type Starlike Harmonic Functions Involving
*q*-Srivastava–Attiya Operator

G Murugusundaramoorthy, K Vijaya, D Breaz, LI Cotrlǎ

Mathematics 11 (23), 4711 2023 - Bi-Univalent Functions Based on Binomial Series-Type Convolution Operator Related with Telephone Numbers

H Bayram, K Vijaya, G Murugusundaramoorthy, S Yalın

Axioms 12 (10), 951 2023 - Φ-like analytic functions associated with a vertical domain

S Araci, KR Karthikeyan, G Murugusundaramoorthy, B Khan

Math. Inequal. Appl 26, 935-949 2023 - Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)

G Murugusundaramoorthy, T Bulboacă

Mathematica Slovaca 73 (5), 1183-1196 2023 - Harmonic functions associated with Pascal distribution series

BA Frasin, MO Oluwayemi, S Porwal, G Murugusundaramoorthy

Scientific African 21, e01876 2023 - On -pseudo starlike functions associated with vertical strip domain

J Sokł, G Murugusundaramoorthy, K Vijaya

Asian-European Journal of Mathematics 16 (08), 2350135 2023 - Gamma-Bazilevic functions related with generalized telephone numbers

G Murugusundaramoorthy, H Ahmad

arXiv preprint arXiv:2308.00238 2023 - COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH THE GEGENBAUER POLYNOMIAL

G Murugusundaramoorthy, H Gney

Palestine Journal of Mathematics 12 (3) 2023 - Sakaguchi Type Starlike Functions Related with Miller-Ross-Type Poisson Distribution in Janowski Domain

SM El-Deeb, A Alharbi, G Murugusundaramoorthy

Mathematics 11 (13), 2918 2023 - Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients

G Murugusundaramoorthy, K Vijaya, T Bulboacă

Mathematics 11 (13), 2857 2023 - Certain Class of Bi-Univalent Functions Defined by Sălăgean
*q*-Difference Operator Related with Involution Numbers

D Breaz, G Murugusundaramoorthy, K Vijaya, LI Cotrlǎ

Symmetry 15 (7), 1302 2023 - An application of the power series distribution for univalent function classes with positive coefficients

M Gangadharan, S Yalın, E Yaşar, S akmak

International Journal of Nonlinear Analysis and Applications 14 (5), 259-265 2023 - Pascu-Rnning Type Meromorphic Functions Based on Sălăgean-Erdly–Kober Operator

SM El-Deeb, G Murugusundaramoorthy, K Vijaya, A Alburaikan

Axioms 12 (4), 380 2023 - On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli

L Gruszecki, A Lecko, G Murugusundaramoorthy, S Sivasubramanian

Symmetry 15 (4), 875 2023

- Salagean-type harmonic univalent functions.

JM Jahangiri, G Murugusundaramoorthy, K Vijaya

Southwest Journal of Pure and Applied Mathematics [electronic only] 2002, 77-82 2002

Citations: 156 - Certain subclasses of bi-univalent functions associated with the Hohlov operator

HM Srivastava, G Murugusundaramoorthy, N Magesh

Global J. Math. Anal 1 (2), 67-73 2013

Citations: 123 - Coefficient bounds for certain subclasses of bi-univalent function

G Murugusundaramoorthy, N Magesh, V Prameela

Abstract and Applied Analysis 2013 2013

Citations: 121 - Neighborhoods of certain classes of analytic functions of complex order

G Murugusundaramoorthy, HM Srivastava

J. Inequal. Pure Appl. Math 5 (2), 1-8 2004

Citations: 107 - Subclasses of uniformly convex and uniformly starlike functions

KG Subramanian

Mathematica japonicae 42 (3), 517-522 1995

Citations: 102 - Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series

G Murugusundaramoorthy, K VİYAJA

Hacettepe Journal of Mathematics and Statistics 45 (4), 1101-1107 2016

Citations: 87 - Hypergeometric functions in the parabolic starlike and uniformly convex domains

HM Srivastava, G Murugusundaramoorthy, S Sivasubramanian

Integral Transforms and Special Functions 18 (7), 511-520 2007

Citations: 84 - COEFFICIENT INEQUALITIES FOR CERTAIN CLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH HANKEL DETERMINANT (DEDICATED IN OCCASION OF THE 65-YEARS OF PROFESSOR RK RAINA)

G Murugusundaramoorthy, N Magesh

Bulletin of Mathematical Analysis and Applications 1 (3), 85-89 2009

Citations: 83 - Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers

H Gney, G Murugusundaramoorthy, J Sokł

Acta Universitatis Sapientiae, Mathematica 10 (1), 70-84 2018

Citations: 81 - Subclasses of starlike and convex functions involving Poisson distribution series

G Murugusundaramoorthy

Afrika Matematika 28 (7), 1357-1366 2017

Citations: 66 - Sigmoid function in the space of univalent λ-pseudo starlike functions

G Murugusundaramoorthy, T Janani

Int. J. Pure Appl. Math 101 (1), 33-41 2015

Citations: 54 - Neighbourhoods and partial sums of starlike functions based on Ruscheweyh derivatives

T Rosy, KG Subramanian, G Murugusundaramoorthy

J. Ineq. pure and appl. Math 4 (4) 2003

Citations: 54 - Coefficient estimates for some families of bi-Bazilevic functions of the Ma-Minda type involving the Hohlov operator

HM Srivastava, G Murugusundaramoorthy, K Vijaya

J. Class. Anal 2 (2), 167-181 2013

Citations: 49 - Coefficient bounds for bi-univalent analytic functions associated with Hohlov operator

T Panigrahi, G Murugusundaramoorthy

Proceedings of the Jangjeon Mathematical Society 16 (1), 91-100 2013

Citations: 45 - A certain family of bi-univalent functions associated with the Pascal distribution series based upon the Horadam polynomials

HM Srivastava, AK Wanas, G Murugusundaramoorthy

Surv. Math. Appl 16, 193-205 2021

Citations: 43 - On certain subclasses of analytic functions associated with hypergeometric functions

G Murugusundaramoorthy, N Magesh

Applied mathematics letters 24 (4), 494-500 2011

Citations: 41 - Faber polynomial coefficient estimates of bi-close-to-convex functions connected with the Borel distribution of the Mittag-Leffler type

HM Srivastava, G Murugusundaramoorthy, SM El-Deeb

J. Nonlinear Var. Anal 5 (1), 103-118 2021

Citations: 40 - Fekete–Szeg functional problems for some subclasses of bi-univalent functions defined by Frasin differential operator

F Yousef, T Al-Hawary, G Murugusundaramoorthy

Afrika Matematika 30, 495-503 2019

Citations: 39 - A class of Ruscheweyh-type harmonic univalent functions with varying arguments

G Murugusundaramoorthy

Southwest J. Pure Appl. Math 2, 90-95 2003

Citations: 39 - Coefficient estimate of bi-univalent functions of complex order associated with the Hohlov operator

Z Peng, G Murugusundaramoorthy, T Janani

J. Complex Anal 2014, 693908 2014

Citations: 38