Browsing by Author "Ahuja, Om P."

Now showing 1 - 8 of 8

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Analytic Functions With Conic Domains Associated With Certain Generalized q-integral Operator
(Korean Mathematical Society, 2023) Ahuja, Om P.; ÇETİNKAYA, ASENA; Jain, Naveen Kumar
In this paper, we define a new subclass of k-uniformly starlike functions of order-gamma (0 <= gamma < 1) by using certain generalized q integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q sufficient coefficient condition, q-Fekete-Szego inequalities, q-Bieberbach De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order-gamma by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.
Open Access
Faber Polynomial Expansion for a New Subclass of Bi-univalent Functions Endowed with (p,q) Calculus Operators
(Fuat Usta, 2021) Ahuja, Om P.; ÇETİNKAYA, ASENA
In this paper, we use the Faber polynomial expansion techniques to get the general TaylorMaclaurin coefficient estimates for |an|, (n ≥ 4) of a generalized class of bi-univalentfunctions by means of (p,q)−calculus, which was introduced by Chakrabarti and Jagannathan. For functions in such a class, we get the initial coefficient estimates for |a2| and|a3|. In particular, the results in this paper generalize or improve (in certain cases) thecorresponding results obtained by recent researchers.
Restricted
Geometric Properties of Starlikeness Involving Hyperbolic Cosine Function
(Korean Mathematical Society, 2024) Ahuja, Om P.; ÇETİNKAYA, ASENA; Kumar, Sushil
In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, BriotBouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.
Restricted
q-Analog of Prestarlike Functions
(Springer International Publishing, 2024) Verma, Sarika; Kumar, Raj; Ahuja, Om P.; ÇETİNKAYA, ASENA
We introduce a class Rαq of q-prestarlike functions of order α by using q-difference operator. We obtain necessary and sufficient conditions involving convolution for functions to be in the class Rαq. We prove that the well-known class of analytic prestarlike functions, Rα, is properly contained in Rαq. Apart from finding bounds on some initial coefficients of functions in the class Rαq, we also investigate some convolution properties of functions in the class Rαq. The results of the present manuscript essentially generalize some well-known results in the literature. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
Open Access
Salagean-Type Harmonic Multivalent Functions Defined by Q-Difference Operator
(Univ Babes-Bolyai, 2022) Ahuja, Om P.; ÇETİNKAYA, ASENA; Mert, Oya
We introduce a new subclass of Salagean-type harmonic multivalent functions by using q-difference operator. We investigate sufficient coefficient es-timates, distortion bounds, extreme points, convolution properties and neighbor-hood for the functions belonging to this function class.
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Spirallike and robertson functions of complex order with bounded boundary rotations
(2019-06) Çetinkaya, Asena; Kahramaner, Yasemin; Ahuja, Om P.
Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.
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A Survey on the Theory of Integral and Related Operators in Geometric Function Theory
(Springer, 2021) Ahuja, Om P.; ÇETİNKAYA, ASENA
A brief tour of more than one hundred years of the historical development of some of the popular integral and related operators in Geometric Function Theory (GFT) is given in this article. The strengths and discovery of the methods used in these operators lie in their ability to unify a large number of diverse operators and results. We also address some of the q- analogues of the integral operators in GFT. Since there are several surveys and books in GFT, we present here only a selection of the results related to our precise objectives. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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Use of quantum calculus approach in Mathematical Sciences and its role in Geometric Function Theory
(AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA, 2019) Çetinkaya, Asena; Ahuja, Om P.
The study of 300 years old history of quantum calculus or q-calculus or q-disease, since the Bernoulli and Euler, is often considered to be one of the most di ffi cult subjects to engage in mathematics. Nowadays there is a rapid growth of activities in the area of q-calculus due to its applications in various fields such as mathematics, mechanics, and physics. The history of study of q-calculus may be illustrated by its wide variety of applications in quantum mechanics, analytic number theory, theta functions, hypergeometric functions, theory of finite di ff erences, gamma function theory, Bernoulli and Euler polynomials, Mock theta functions, combinatorics, umbral calculus, multiple hypergeometric functions, Sobolev spaces, operator theory, and more recently in the theory of analytic and harmonic univalent functions. In q-calculus, we are generally interested in q-analogues that arise naturally, rather than in arbitrarily contriving q-analogues of known results. While focusing on excitement and romance with development of q-calculus and its applications in certain fields of mathematical sciences and physics, we will also look at q-analogues of some of the recent results in geometric function theory and, in particular, theory of analytic and harmonic univalent functions in the unit disc.