Certain Properties ofq-Hypergeometric Functions

Abstract

The quotients of certainq-hypergeometric functions are presented asg-fractions which converge uniformly in the unit disc. These results lead to the existence of certainq-hypergeometric functions in the class of eitherq-convex functions,PCq, orq-starlike functionsPSq*.

On Fekete-Szegö Problems for Certain Subclasses Defined byq-Derivative

“…Quite a number of great mathematicians studied the concepts of -derivative, for example, by Gasper and Rahman [3], Aral et al [4], Li et al [5], and many others (see [6][7][8][9][10][11][12][13][14][15]). …”

Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions

“…A background of the usage of the q-calculus in the context of Geometric Funciton Theory was actually provided and the basic (or q-) hypergeometric functions were first used in Geometric Function Theory by Srivastava (see, for details, [6]). Some recent investigations associated with the q-derivative operator D q in analytic function theory can be found in [7][8][9][10][11][12][13] and the references cited therein. Definition 6.…”

Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

“…Now, we recall some basic concepts and definitions related to q-derivative, to be used in this work. For more details, see References [3,[14][15][16].…”

“…For more detail, see [20]. From Equations (14) and (15), it is clear that S * q (µ) and C q (µ) are subclasses of the class A.…”