The Order of Strongly Starlikeness of the Generalized α-Convex Functions

Abstract

We consider the order of the strongly-starlikeness of the generalized α -convex functions. Some sufficient conditions for functions to be p-valently strongly-starlike are given.

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

“…Due to the applications of q-analysis in mathematics and other fields, numerous researchers [3,[5][6][7][8][9][10][11][12][13][14] did some significant work on q-calculus and studied its several other applications. Recently, Srivastava [15] in his survey-cum-expository article, explored the mathematical application of q-calculus, fractional qcalculus and fractional q-differential operators in geometric function theory. Keeping in view the significance of q-operators instead of ordinary operators and due to the wide range of applications of q-calculus, many researchers comprehensively studied q-calculus such as Srivastava et al [16], Muhammad and Darus [17], Kanas and Reducanu [18] and Muhammad and Sokol [19].…”

“…Keeping in view the significance of q-operators instead of ordinary operators and due to the wide range of applications of q-calculus, many researchers comprehensively studied q-calculus such as Srivastava et al [16], Muhammad and Darus [17], Kanas and Reducanu [18] and Muhammad and Sokol [19]. Motivated by [15][16][17][18][19][20][21], we consider subfamilies of q-convex functions and q-close to convex functions with respect to Janowski functions connected with q-conic domain.…”