New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

Abstract

Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator Dq,λmρ,σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ−1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies.

A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q̧-Calculus

“…Recently, Srivastava provided a comprehensive survey that explains the mathematical foundations and practical applications of q ¸-derivative operators, within the context of geometric function theory [15]. For those interested in delving deeper into q ¸-calculus and its implications in this field, an abundance of research is at one's disposal, starting with classical publications [16,17], continuing with studies like [18][19][20] and considering very recent research outcome on the topic like [21][22][23][24][25][26][27][28].…”

A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via q̧-Calculus

“…Recently, Srivastava provided a comprehensive survey that explains the mathematical foundations and practical applications of fractional q ¸-derivative operators, within the context of geometric function theory [17]. For those interested in delving deeper into q ¸-calculus and its implications in this field, an abundance of research is at one's disposal, starting with classical publications [18,19], continuing with studies like [20][21][22][23], and considering very recent research outcomes on the topic like [24][25][26][27][28][29][30][31][32].…”

New Uses of q-Generalized Janowski Function in q-Bounded Turning Functions

“…Similarly, using ( 16) and ( 19) while referencing (20) and (22) to calculate l 4 results in the following expression:…”

“…Zang and colleagues [17] employed q-calculus symbols and subordination methods to establish a broad conic region, which was then utilized to analyze the category of q-starlike functions. Several authors have recently conducted studies on the categories of q-starlike functions, as referenced in articles [18][19][20][21][22][23]. In order to research different categories of analytic and bi-univalent functions, the initial step is to establish the definition of the q-difference operator.…”