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
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
G. Murugusundaramoorthy, K. Vijaya, and Luminiţa-Ioana Cotîrlǎ
Springer Science and Business Media LLC
Ibtisam Aldawish, Hari M. Srivastava, Sheza M. El-Deeb, Gangadharan Murugusundaramoorthy, and Kaliappan Vijaya
MDPI AG
In this study, we present two novel subclasses of bi-univalent functions defined in the open unit disk, utilizing Liouville–Caputo fractional derivatives. We find constraints on initial Taylor coefficients |c2|, |c3| for functions in these subclasses of bi-univalent functions. Additionally, by using the values of a2,a3 we determine the Fekete–Szegö inequality results. Moreover, a few new subclasses are deduced that have not been studied in relation to Liouville–Caputo fractional derivatives so far. The implications of the results are also emphasized. Our results are concrete examples of several earlier discoveries that are not only improved but also expanded upon.
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.
G. Murugusundaramoorthy and H. Ö. Güney
Springer Science and Business Media LLC
Timilehin Gideon Shaba, Sibel Yalçin, Gangadharan Murugusundaramoorthy, and Maslina Darus
Springer Science and Business Media LLC
Kadhavoor R. Karthikeyan, Daniel Breaz, Gangadharan Murugusundaramoorthy, and Ganapathi Thirupathi
MDPI AG
Using the concepts of multiplicative calculus and subordination of analytic functions, we define a new class of starlike bi-univalent functions based on a symmetric operator, which involved the three parameter Mittag-Leffler function. Estimates for the initial coefficients and Fekete–Szegő inequalities of the defined function classes are determined. Moreover, special cases of the classes have been discussed and stated as corollaries, which have not been discussed previously.
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.
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.
G. Murugusundaramoorthy and K. Vijaya
Vladikavkaz Scientific Centre of the Russian Academy of Sciences
The Mittag-Leffler~\\cite{mit} function ascends naturally in the solution of fractional order differential and integral equations, and exclusively in the studies of fractional generalizing of kinetic equation, random walks, L\\'{e}vy flights, super-diffusive transport and in the study of complex systems. In the present investigation, the authors define a new class of meromorphic functions defined in the punctured unit disk $\\Delta^*:= \\{z\\in\\mathbb{C}: 0<|z|<1\\}$ based on Mittag-Leffler function denoted by $\\mathfrak{M}^{\\tau,\\kappa}_{\\varsigma,\\varrho}(\\vartheta,\\wp)$. We discuss its characteristic properties like coefficient inequalities, growth and distortion inequalities, as well as closure results for $f\\in\\mathfrak{M}^{\\tau,\\kappa}_{\\varsigma,\\varrho}(\\vartheta,\\wp)$extensively. Properties of a certain integral operator and its inverse defined on the new class $\\mathfrak{M}^{\\tau,\\kappa}_{\\varsigma,\\varrho}(\\vartheta,\\wp)$ are also discussed. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also prove a Property using an integral operator and its inverse defined on the new class.We also establish some results concerning neighborhoods and the partial sums of meromorphic functions in this new class. We also state some new subclasses and its characteristic properties by specializing the parameters which are new and not studied in association with Mittag-Leffler functions.
Sa’ud Al-Sa’di, Kaliyappan Vijaya, and Gangadharan Murugusundaramoorthy
Wiley
Telephone numbers defined through the recurrence relation for n ≥ 2, with initial values of . The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit disk by utilizing the normalized Rabotnov function and defining a new linear operator subordinated with generalized telephone numbers. We also obtain bounds of the initial Taylor–Maclaurin coefficients, |a2| and |a3|, for these functions and determine the Fekete–Szegö inequalities. In addition, several related corollaries are presented. These findings are based on the recent study of the Rabotnov function and demonstrate its significance in the field.
S. Ashwini, M. Ruby Salestina, and G. Murugusundaramoorthy
SCIK Publishing Corporation
The purpose of this paper is to consider coefficient estimates for q-starlike function with respect to symmetric points associated with sine function \\(\\mathcal{SS}^*_ q(1+sin(z))\\) consisting of analytic functions \\(f\\) normalized by \\(f(0)=f'(0)-1=0\\) in the open unit disk \\(\\mathcal{U}_d=\\{ z:z\\in \\mathbb{C}\\quad \\text{and}\\quad \\left\\vert z\\right\\vert <1\\}\\) satisfying the condition \\(\\dfrac{2[zD_qf(z)]}{f(z)-f(-z)}\\prec{1+sin(z)}=\\psi(z)\\), for all \\(z\\in\\mathcal{U}_d\\) to derive certain coefficient estimates \\(b_2,b_3\\) etc and Fekete-Szeg\\"{o} inequality for \\(f\\in\\mathcal{SS}^*_q(1+sin(z)).\\) Further to investigate the possible upper bound of third order Hankel determinant and also the Zalcman functional for \\(f\\in\\mathcal{SS}^*_q(1+sin(z))\\).
Pinhong Long, Jinlin Liu, and Murugusundaramoorthy Gangadharan
Springer Science and Business Media LLC
Gangadharan Murugusundaramoorthy, Alina Alb Lupas, Alhanouf Alburaikan, and Sheza M. El-Deeb
Walter de Gruyter GmbH
Abstract 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. The objective of this article is to define the families of Sakaguchi-type starlike functions with respect to symmetric points based on q q -operator and to investigate the precise boundaries for a range of issues, including the first three initial coefficient estimates, Fekete-Szegö type and the Zalcman inequalities by subordinating to the function of the three leaves. Additionally, we discussed initial coefficients and Fekete-Szegö type inequalities for functions of the form ℱ − 1 {{\\mathcal{ {\\mathcal F} }}}^{-1} and z ℱ ( z ) \\frac{z}{{\\mathcal{ {\\mathcal F} }}\\left(z)} and 1 2 log ℱ ( z ) z \\frac{1}{2}\\log \\left(\\phantom{\\rule[-0.75em]{}{0ex}},\\frac{{\\mathcal{ {\\mathcal F} }}(z)}{z}\\right) linked with the function of the three leaves.
M. Nandeesh, M. Ruby Salestina, Archana, and G. Murugusundaramoorthy
SCIK Publishing Corporation
The fundamental focus of researching coefficient problems for various families of univalent functions involves characterizing the coefficients of functions within a particular family based on the coefficients of Caratheodory functions. Consequently, by employing known inequalities for the class of Caratheodory functions, coefficient functionals can be scrutinized. This study will tackle several coefficient problems by applying the methodology to the aforementioned family of functions. Our investigation centers on the family of Sokol-Stankiewicz star-like functions which is defined in the open unit disk D. We explore the bounds of certain initial coefficients, including the Fekete-Szego inequality and other results concerning logarithmic coefficients for functions within this class.
, V. Prakash, S. Sivasubramanian, , G. Murugusundaramoorthy, and
Editura Academiei Române
Classes of analytic functions for which both $f$ and $f^{\\prime}$ are univalent in the open unit disc $\\mathbb{E} = \\left\\{z : |z| 1\\right\\}$ was investigated earlier by Silverman in 1987. However, the application of Gaussian hypergeometric functions on the classes of analytic functions for which both $f$ and $f^{\\prime}$ are univalent in the open unit disc $\\mathbb{E}$ is not being studied in the literature. By exploring this, we investigate the necessary and sufficient conditions and inclusion relations for certain function involving Gaussian hypergeometric functions to be in few subclasses of analytic functions for which both $f$ and $f^{\\prime}$ are univalent in the open unit disc $\\mathbb{E} $ in this article. Further, we consider an integral operator related to Gaussian hypergeometric functions and several mapping properties are discussed. We also pointed out certain corollaries and consequences of the main results.
GANGADHARAN MURUGUSUNDARAMOORTHY, ALINA ALB LUPAS, KALIAPPAN VIJAYA, MAJEED AHMAD YOUSIF, PSHTIWAN OTHMAN MOHAMMED, THOMAS ROSY, and YASSER SALAH HAMED
World Scientific Pub Co Pte Ltd
Recent studies in analytic functions have increasingly focused on shell-like domains and their connections to fractional operators. This work introduces a novel class of analytic functions, [Formula: see text], and explores the Fekete–Szegö inequality and new coefficient values for this class. To align with fractional analysis, we explore the applications of the Erdélyi–Kober fractional integral operator within this framework. Additionally, we examine the function [Formula: see text] and its inverse [Formula: see text], extending the analysis to fractional-order settings. A new class, [Formula: see text], is defined and studied in relation to convolution with normalized analytic functions. Notably, Fekete–Szegö inequalities are derived for specific subclasses involving the Poisson distribution series, demonstrating how fractional calculus enriches geometric function theory and extends its applications across broader mathematical and physical domains. Recent studies in analytic functions have increasingly focused on shell-like domains. An innovative class of analytic functions is presented in this study, [Formula: see text], and the Fekete–Szegö inequality is investigated for this class and new coefficient estimates. We extend our analysis to include the function [Formula: see text] and its inverse [Formula: see text]. Additionally, we define and study the class [Formula: see text] and explore its applications to functions obtained by convolution with normalized analytic functions. Notably, we expand our method to more general function theory applications by deriving Fekete–Szegö inequalities for particular subclasses of functions defined via the Poisson distribution series.
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.
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.