Some General Classes of q-Starlike Functions Associated with the Janowski Functions

Abstract

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this paper, we first investigate the relationship between various known classes of q-starlike functions that are associated with the Janowski functions. We then introduce and study a new subclass of q-starlike functions that involves the Janowski functions. We also derive several properties of such families of q-starlike functions with negative coefficients including (for example) distortion theorems.

Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

“…This domain describes the conic type domain; for details, see [38]. Note that (i) When q → 1, then domain Ω κ,q (λ, α) reduces to the domain Ω κ (λ, α) (see [39]).…”

Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach

“…In recent years, there is a great development of geometric function theory because of using quantum calculus approach. In particular, Srivastava et al [18] found distortion and radius of univalence and starlikenss for several subclasses of q-starlike functions with negative coefficients. They [19] also determined sufficient conditions and containment results for the different types of k-uniformly q-starlike functions.…”

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

“…In recent years, several interesting subclasses of analytic and multivalent functions have been introduced and investigated (see, for example, [9][10][11][12][13][14][15][16]). Motivated and inspired by recent and ongoing research, we introduce and investigate here a new subclass of close-to-convex functions in U which are associated with the lemniscate of Bernoulli by using some techniques similar to those that were used earlier by Sokół and Stankiewicz (see [3]).…”