On Quantum Differential Subordination Related with Certain Family of Analytic Functions

Abstract

Recently, there is a rapid increase of research in the area of Quantum calculus (known as q -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of q -conic domains of Janowski type as well as q - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of α -convex and quasi-convex functions. Furthermore, a coefficient inequality, sufficiency criteria, and covering results for these novel classes are derived. Besides, some remarkable consequences of our investigation are highlighted.

On Lemniscate of Bernoulli of q-Janowski type

“…where we have used condition (12). This proves (16). Furthermore, condition (17) is achieved by setting…”

“…Moreover, Raza and Malik [8] proved the third Hankel determinant associated with L * . For other related works, see [9,10,11,12,13,14,15,16,17,18,19,20] for details.…”

Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain

“…Due to its numerous uses in mathematical analysis and the physical sciences, such as q-difference operators, fractional and q-symmetric fractional q-calculus, optimal control, qsymmetric functions, and q-integral equations, the q-derivative has undergone accelerated development in a variety of scientific fields in recent decades (for more details, see [1][2][3][4][5][6][7][8]). Jackson introduces the q-difference operator and describes several applications of the qintegral and q-derivative in [9] (see also [10]).…”

A Study of q-analogue of the analytic characterization of Limacon functions

“…The development of this concept in Complex analysis is traced to the work of Ismail et al [1]. As such, many subclasses of Ma and Minda classes correlated with the idea of quantum calculus have been illustrated in various distinct directions (see [6,10,15,21,22]). For example, Srivastava et al [23] introduce certain higher-order q-derivatives, which were used to study new subclasses of multivalent q-starlike functions that are associated with the Janowski functions and involving certain conic domains.…”