Certain subclasses of analytic functions associated with fractional $q$-calculus operators

Abstract

We first define the $q$-analogue operators of fractional calculus which are then used in defining certain classes of functions analytic in the open disk. The results investigated for these classes of functions include the coefficient inequalities and some distortion theorems. The results provide extensions of various known results in the $q$-theory of analytic functions. Special cases of our results are pointed out briefly.

Subordination Conditions for a Class of Non-Bazilevič Type Defined by Using Fractional Q-Calculus Operators

“…Purohit and Raina [21] used fractional q-calculus operators in investigating certain classes of functions which are analytic in the open disk. Recently, many authors have introduced new classes of analytic functions using q-calculus operators.…”

“…Recently, many authors have introduced new classes of analytic functions using q-calculus operators. For some recent investigations on the classes of analytic functions defined by using qcalculus operators and related topics, we refer the reader to [3,17], [22]- [25], [29,30] and the references cited therein. In the present paper, we aim at introducing a new class of non-Bazilevič type involving fractional q-calculus operators.…”

“…We now define the fractional q-calculus operators of a complex-valued function f (z), which were recently studied by Purohit and Raina [21].…”

ON CERTAIN GENERALIZED q-INTEGRAL OPERATORS OF ANALYTIC FUNCTIONS

“…Recently, S. D. Purohit and R. K. Raina [18], [19], [20] and [21] have used the fractional q-calculus operators in investigating certain subclasses of functions which are analytic in the open unit disk U. S. D. Purohit [17] also studied similar work and considered new classes of multivalently analytic functions in the open unit disk. The aim of this paper is to consider a linear multiplier fractional q-differintegral operator and to define certain new subclasses of functions which are p-valent and analytic in the open unit disk.…”

“…In the following, we define the fractional q-calculus operators of a complexvalued function f (z), which were recently studied by S. D. Purohit and R. K. Raina [18].…”