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
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
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.
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.
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.
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.
Adnan Ghazy Al Amoush and Gangadharan Murugusundaramoorthy
Springer Science and Business Media LLC
Sevtap Sümer Eker, Gangadharan Murugusundaramoorthy, Bilal Şeker, and Bilal Çekiç
Springer Science and Business Media LLC
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.
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.