Basic and fractional q-calculus and associated Fekete-Szegő problem for p-valently q-starlike functions and p-valently q-convex functions of complex order
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In this article, the Taylor-Maclaurin coefficients fakg1kDpC1 of each of these subclasses of p-valently analytic functions were derived for the Fekete-Szegő functional given by ˇ̌̌ apC2 a 2 pC1.Abstract:
In this paper, we introduce and study some subclasses of p-valently analytic functions in the open unit disk U by applying the q-derivative operator and the fractional q-derivative operator in conjunction with the principle of subordination between analytic functions. For the Taylor-Maclaurin coefficients fakg1kDpC1 of each of these subclasses of p-valently analytic functions, we derive sharp bounds for the Fekete-Szegő functional given by ˇ̌̌ apC2 a 2 pC1 ˇ̌̌ : Relevant connections of the results presented in this paper with those derived in earlier works are also considered. 2010 Mathematics Subject Classification: 26A33; 33C20; 30C45; 30C50read more
Citations
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Journal ArticleDOI
Operators of Basic (or q-) Calculus and Fractional q-Calculus and Their Applications in Geometric Function Theory of Complex Analysis
TL;DR: In this article, the authors define the subclasses of normalized analytic functions with complex order and negative coefficients and derive their associated coefficient estimates, radii of close-to-convexity, starlikeness and convexity.
Journal ArticleDOI
Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function
Hari M. Srivastava,Hari M. Srivastava,Hari M. Srivastava,Bilal Khan,Nazar Khan,Muhammad Tahir,Sarfraz Ahmad,Nasir Khan +7 more
TL;DR: In this article, the upper bound of the third-order Hankel determinant H 3 (1 ) for functions belonging to the q-star-like function class S ⁎ (L, q ) is derived.
Journal ArticleDOI
An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers
TL;DR: A new class of q-starlike functions associated with k-Fibonacci numbers is defined, a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations.
Journal ArticleDOI
Partial sums of generalized q -Mittag-Leffler functions
TL;DR: In this article, lower bounds for the ratio of normalized q-Mittag-Leffler functions and their sequences of partial sums are given, and various corollaries and consequences of the main results are considered.
Journal ArticleDOI
The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator
TL;DR: This paper introduces an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution to study the subordination-preserving properties and their dual problems.
References
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Book
Basic Hypergeometric Series
George Gasper,Mizan Rahman +1 more
TL;DR: In this article, the Askey-Wilson q-beta integral and some associated formulas were used to generate bilinear generating functions for basic orthogonal polynomials.
Book
Differential Subordinations: Theory and Applications
TL;DR: Preliminaries theory of second-order differential subordinations applications of first order differential subordination applications of second order differential sub-ordination applications in other fields as mentioned in this paper ; convexity of Bernoulli function.