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
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.
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.
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.
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.
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.
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.
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.
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.
G. Murugusundaramoorthy, N. E. Cho, and K. Vijaya
Springer Science and Business Media LLC
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>
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>
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.
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.
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.
Serkan Araci, K. R. Karthikeyan, G. Murugusundaramoorthy, and Bilal Khan
Element d.o.o.
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.
B.A. Frasin, M.O. Oluwayemi, S. Porwal, and G. Murugusundaramoorthy
Elsevier BV
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.
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.
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.
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.