Subclasses of Starlike Functions Associated with Fractional q-Calculus Operators

Abstract

Making use of fractional q-calculus operators, we introduce a new subclass ℳq(λ,γ,k) of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in ℳq(λ,γ,k). Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in ℳq(λ,γ,k).

Certain Properties of Some Families of Generalized Starlike Functions with respect toq-Calculus

“…Recently, EsraÖzkan Uçar [13] studied the coefficient inequality for -closed-to-convex functions with respect to Janowski starlike functions. Here, many newsworthy results related to -calculus and subclasses of analytic functions theory are studied by various authors (see [14][15][16][17][18][19][20][21]). …”

Certain Classes of Analytic Functions Bound with Kober Operators in q -Calculus

“…e applications of fractional q-calculus operators have been investigated by Purohit and Raina [4] to describe several new classes of analytic functions in open disk U � ξ ∈ C: |ξ| < 1 { }. Moreover, Murugusundaramoorthy et al [5], Purohit [6], and Purohit and Raina [4,7] gave related work and added various classes of univalent and multivalently analytic functions in open unit disk U. Several others have also released new classes of analytical functions with the resources of q-calculus operators.…”

Subordination Conditions for a Class of Non-Bazilevič Type Defined by Using Fractional 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.…”