Murugusundaramoorthy Gangadharan
@vit.ac.in
Professor(Higher Academic Grade)
Vellore Institute of Technology (VIT)
EDUCATION
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
RESEARCH INTERESTS
Complex Analysis-Geometric Function Theory
236
Scopus Publications
3977
Scholar Citations
31
Scholar h-index
100
Scholar i10-index
Scopus Publications
- Pseudo starlike functions involving convex combination of two starlike functions
K. R. Karthikeyan and G. Murugusundaramoorthy
Taru Publications
In this paper, we introduce a new class of functions involving a familiar analytic characterization that was used to obtain sufficient conditions for starlikeness. We have discussed the impact of the convex combination of two starlike functions. The results obtained here extend or unify the various other well-known and new results. - On a New Class of Concave Bi-Univalent Functions Associated with Bounded Boundary Rotation
Prathviraj Sharma, Srikandan Sivasubramanian, Gangadharan Murugusundaramoorthy, and Nak Eun Cho
MDPI AG
In this research article, we introduce a new subclass of concave bi-univalent functions associated with bounded boundary rotation defined on an open unit disk. For this new class, we make an attempt to find the first two initial coefficient bounds. In addition, we investigate the very famous Fekete–Szegö inequality for functions belonging to this new subclass of concave bi-univalent functions related to bounded boundary rotation. For some particular choices of parameters, we derive the earlier estimates on the coefficient bounds, which are stated at the end. - q-analogue of a p-harmonic mapping
Saurabh Porwal, Omendra Mishra, and G. Murugusundaramoorthy
World Scientific Pub Co Pte Ltd
The primary objective of this paper is to explore a novel subclass [Formula: see text] of [Formula: see text]-harmonic mappings, along with the associated subclass [Formula: see text]. We demonstrate that the mapping [Formula: see text] is both univalent and sense-preserving within the unit disk [Formula: see text]. Furthermore, we determine the extreme points of [Formula: see text] and establish that [Formula: see text] is defined. Additional results include the derivation of distortion bounds, the convolution condition, and the convex combination for this subclass. Finally, we examine the class-preserving integral operator and introduce a [Formula: see text]-Jackson type integral operator. - Faber Polynomial Coefficient Estimates of m-Fold Symmetric Bi-Univalent Functions with Bounded Boundary Rotation
Anandan Murugan, Srikandan Sivasubramanian, Prathviraj Sharma, and Gangadharan Murugusundaramoorthy
MDPI AG
In the current article, we introduce several new subclasses of m-fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk D. Utilizing the Faber polynomial expansion, we derive upper bounds for the coefficients |bmk+1| and establish initial coefficient bounds for |bm+1| and |b2m+1|. Additionally, we explore the Fekete–Szegö inequalities applicable to the functions that fall within these newly defined subclasses. - On λ-Pseudo Bi-Starlike Functions Related to Second Einstein Function
Alaa H. El-Qadeem, Gangadharan Murugusundaramoorthy, Borhen Halouani, Ibrahim S. Elshazly, Kaliappan Vijaya, and Mohamed A. Mamon
MDPI AG
A new class BΣλ(γ,κ) of bi-starlike λ-pseudo functions related to the second Einstein function is presented in this paper. c2 and c3 indicate the initial Taylor coefficients of ϕ∈BΣλ(γ,κ), and the bounds for |c2| and |c3| are obtained. Additionally, for ϕ∈BΣλ(γ,κ), we calculate the Fekete–Szegö functional. - Attributes of Subordination of a Specific Subclass of p-Valent Meromorphic Functions Connected to a Linear Operator
Rabha M. El-Ashwah, Alaa Hassan El-Qadeem, Gangadharan Murugusundaramoorthy, Ibrahim S. Elshazly, and Borhen Halouani
MDPI AG
This work examines subordination conclusions for a specific subclass of p-valent meromorphic functions on the punctured unit disc of the complex plane where the function has a pole of order p. A new linear operator is used to define the subclass that is being studied. Furthermore, we present several corollaries with intriguing specific situations of the results. - Applications of Mittag–Leffler Functions on a Subclass of Meromorphic Functions Influenced by the Definition of a Non-Newtonian Derivative
Daniel Breaz, Kadhavoor R. Karthikeyan, and Gangadharan Murugusundaramoorthy
MDPI AG
In this paper, we defined a new family of meromorphic functions whose analytic characterization was motivated by the definition of the multiplicative derivative. Replacing the ordinary derivative with a multiplicative derivative in the subclass of starlike meromorphic functions made the class redundant; thus, major deviation or adaptation was required in defining a class of meromorphic functions influenced by the multiplicative derivative. In addition, we redefined the subclass of meromorphic functions analogous to the class of the functions with respect to symmetric points. Initial coefficient estimates and Fekete–Szegö inequalities were obtained for the defined function classes. Some examples along with graphs have been used to establish the inclusion and closure properties. - Applications of Caputo-Type Fractional Derivatives for Subclasses of Bi-Univalent Functions with Bounded Boundary Rotation
Kholood M. Alsager, Gangadharan Murugusundaramoorthy, Adriana Catas, and Sheza M. El-Deeb
MDPI AG
In this article, for the first time by using Caputo-type fractional derivatives, we introduce three new subclasses of bi-univalent functions associated with bounded boundary rotation in an open unit disk to obtain non-sharp estimates of the first two Taylor–Maclaurin coefficients, |a2| and |a3|. Furthermore, the famous Fekete–Szegö inequality is obtained for the newly defined subclasses of bi-univalent functions. Several consequences of our results are pointed out which are new and not yet discussed in association with bounded boundary rotation. Some improved results when compared with those already available in the literature are also stated as corollaries. - Subclasses of Bi-Univalent Functions Connected with Caputo-Type Fractional Derivatives Based upon Lucas Polynomial
Kholood M. Alsager, Gangadharan Murugusundaramoorthy, Daniel Breaz, and Sheza M. El-Deeb
MDPI AG
In the current paper, we introduce new subclasses of analytic and bi-univalent functions involving Caputo-type fractional derivatives subordinating to the Lucas polynomial. Furthermore, we find non-sharp estimates on the first two Taylor–Maclaurin coefficients a2 and a3 for functions in these subclasses. Using the values of a2 and a3, we determined Fekete–Szegő inequality for functions in these subclasses. Moreover, we pointed out some more subclasses by fixing the parameters involved in Lucas polynomial and stated the estimates and Fekete–Szegő inequality results without proof. - Coefficient Functionals of Sakaguchi-Type Starlike Functions Involving Caputo-Type Fractional Derivatives Subordinated to the Three-Leaf Function
Kholood M. Alsager, Sheza M. El-Deeb, Gangadharan Murugusundaramoorthy, and Daniel Breaz
MDPI AG
A challenging part of studying geometric function theory is figuring out the sharp boundaries for coefficient-related problems that crop up in the Taylor–Maclaurin series of univalent functions. Using Caputo-type fractional derivatives to define the families of Sakaguchi-type starlike functions with respect to symmetric points, this article aims to investigate the first three initial coefficient estimates, the bounds for various problems such as Fekete–Szegő inequality, and the Zalcman inequalities, by subordinating to the function of the three leaves domain. Fekete–Szegő-type inequalities and initial coefficients for functions of the form H−1 and ζH(ζ) and 12logHζζ connected to the three leaves functions are also discussed. - 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 - Applications of Noor type Differential Operator on Multivalent Functions
- Bi-univalent functions subordinated to a three leaf function induced by multiplicative calculus
G. Murugusundaramoorthy, K. Vijaya, K. R. Karthikeyan, Sheza M. El-Deeb, and Jong-Suk Ro
American Institute of Mathematical Sciences (AIMS)
<p>Our aim was to develop a new class of bi starlike functions by utilizing the concept of subordination, driven by the idea of multiplicative calculus, specifically multiplicative derivatives. Several restrictions were imposed, which were indeed strict constraints, because we have tried to work within the current framework or the design of analytic functions. To make the study more versatile, we redefined our new class of function with Miller-Ross Poisson distribution (MRPD), in order to increase the study's adaptability. We derived the first coefficient estimates and Fekete-Szegő inequalities for functions in this new class. To demonstrate the characteristics, we have provided a few examples.</p> - CLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE (p, q)–DERIVATIVE OPERATOR FOR GENERALIZED DISTRIBUTION SATISFYING SUBORDINATE CONDITION
- 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. - SUFFICIENT CONDITIONS OF SUBCLASSES OF SPIRAL-LIKE FUNCTIONS ASSOCIATED WITH MITTAG-LEFFLER FUNCTIONS
, GANGADHARAN MURUGUSUNDARAMOORTHY, TEODOR BULBOACĂ, and
University Library in Kragujevac
The purpose of the present paper is to find the sufficient conditions for some subclasses of analytic functions associated with Mittag-Leffler functions to be in subclasses of spiral-like univalent functions. Further, we discuss geometric properties of an integral operator related to Mittag-Leffler functions. - 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.
RECENT SCHOLAR PUBLICATIONS
- INEQUALITIES FORMULATED BY A SPECIAL CLASS OF BAZILEVIČ FUNCTIONS COMBINING THE BELL SERIES
G MURUGUSUNDARAMOORTHY, RW IBRAHIM
Kragujevac Journal of Mathematics 50 (7), 1135-1147 2026 - On a New Class of Concave Bi-Univalent Functions Associated with Bounded Boundary Rotation
P Sharma, S Sivasubramanian, G Murugusundaramoorthy, NE Cho
Mathematics 13 (3), 370 2025 - q– Analogue of a p-harmonic mapping
S Porwal, O Mishra, G Murugusundaramoorthy
Asian-European Journal of Mathematics 2025 - Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions
G Murugusundaramoorthy, LI Cotrlă, D Breaz, SM El-Deeb
Axioms 14 (1), 50 2025 - Fekete-Szeg Inequalities and the Symmetric Toeplitz Determinants for Certain Analytic Function Class Involving q-Differintegral Operator
K PEI, P LONG, J LIU, M GANGADHARAN
Chinese Quarterly Journal of Mathematics 39 (4), 366 2024 - Faber Polynomial Coefficient Estimates of m-Fold Symmetric Bi-Univalent Functions with Bounded Boundary Rotation
A Murugan, S Sivasubramanian, P Sharma, G Murugusundaramoorthy
Mathematics 12 (24), 3963 2024 - Some Evaluations About Coefficients Boundaries for Specific Classes of Bi-Univalent Functions
SM Sowileh, G Murugusundaramoorthy, B Halouani, IS Elshazly, ...
Axioms 13 (12), 821 2024 - Second Hankel Determinant Bound Application to Certain Family of Bi-Univalent Functions
MA Mamon, B Halouani, IS Elshazly, G Murugusundaramoorthy, ...
Axioms 13 (12), 819 2024 - Third-Order Differential Subordination Features of Meromorphic Functions: Erdelyi–Kober Model Integral Operator Application
IS Elshazly, B Halouani, RM El-Ashwah, AH El-Qadeem, ...
Axioms 13 (11), 770 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 - Bi-Starlike Function of Complex Order Involving Mathieu-Type Series in the Shell-Shaped Region
IS Elshazly, G Murugusundaramoorthy, B Halouani, AH El-Qadeem, ...
Axioms 13 (11), 747 2024 - On λ-Pseudo Bi-Starlike Functions Related to Second Einstein Function
AH El-Qadeem, G Murugusundaramoorthy, B Halouani, IS Elshazly, ...
Symmetry 16 (11), 1429 2024 - Attributes of Subordination of a Specific Subclass of p-Valent Meromorphic Functions Connected to a Linear Operator
RM El-Ashwah, AH El-Qadeem, G Murugusundaramoorthy, IS Elshazly, ...
Symmetry 16 (10), 1338 2024 - Applications of Noor type Differential Operator on Multivalent Functions.
FM Sakar, S Hussain, M Naeem, S Khan, G Murugusundaramoorthy, ...
Palestine Journal of Mathematics 13 (4) 2024 - Brief Study On A New Family of Analytic Functions
JO Hamzat, G Murugusundaramoorthy, MO Oluwayemi
Sahand Communications in Mathematical Analysis 21 (4), 109-122 2024 - Applications of Mittag–Leffler Functions on a Subclass of Meromorphic Functions Influenced by the Definition of a Non-Newtonian Derivative
D Breaz, KR Karthikeyan, G Murugusundaramoorthy
Fractal and Fractional 8 (9), 509 2024 - Applications of Caputo-Type Fractional Derivatives for Subclasses of Bi-Univalent Functions with Bounded Boundary Rotation
KM Alsager, G Murugusundaramoorthy, A Catas, SM El-Deeb
Fractal and Fractional 8 (9), 501 2024 - CHEBYSHEV POLYNOMIALS AND BI-UNIVALENT FUNCTIONS ASSOCIATING WITH q-DERIVATIVE OPERATOR.
P Nandini, S Latha, G Murugusundaramoorthy
South East Asian Journal of Mathematics & Mathematical Sciences 20 (2) 2024 - Subclasses of Bi-Univalent Functions Connected with Caputo-Type Fractional Derivatives Based upon Lucas Polynomial
KM Alsager, G Murugusundaramoorthy, D Breaz, SM El-Deeb
Fractal and Fractional 8 (8), 452 2024 - 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
MOST CITED SCHOLAR PUBLICATIONS
- 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: 158 - Coefficient Bounds for Certain Subclasses of Bi‐Univalent Function
G Murugusundaramoorthy, N Magesh, V Prameela
Abstract and Applied Analysis 2013 (1), 573017 2013
Citations: 136 - 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: 124 - 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: 109 - Subclasses of uniformly convex and uniformly starlike functions
KG Subramanian
Mathematica japonicae 42 (3), 517-522 1995
Citations: 104 - Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series
G Murugusundaramoorthy, K Viyaja
Hacettepe Journal of Mathematics and Statistics 45 (4), 1101-1107 2016
Citations: 99 - 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: 92 - 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: 91 - Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers
H Gney, G Murugusundaramoorthy, J Sokł
Acta Univ. Sapient. Math 10 (1), 70-84 2018
Citations: 89 - Subclasses of starlike and convex functions involving Poisson distribution series
G Murugusundaramoorthy
Afrika Matematika 28 (7), 1357-1366 2017
Citations: 77 - 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: 59 - 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: 55 - 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: 54 - Coefficient estimate of biunivalent functions of complex order associated with the Hohlov operator
Z Peng, G Murugusundaramoorthy, T Janani
Journal of Complex analysis 2014 (1), 693908 2014
Citations: 51 - 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 - 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: 48 - Univalent functions with positive coefficients involving Pascal distribution series
T Bulboaca, G Murugusundaramoorthy
Communications of the Korean Mathematical Society 35 (3), 867-877 2020
Citations: 46 - 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: 45 - 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 - Bi-Bazilevic functions of order ϑ+ iδ associated with (p, q)-Lucas polynomials
A Amourah, BA Frasin, G Murugusundaramoorthy, T Al-Hawary
AIMS Math 6 (5), 4296-4305 2021
Citations: 44