Abstract
This paper introduces a new integral operator in q-analog for multivalent functions. Using as an application of this operator, we study a novel class of multivalent functions and define them. Furthermore, we present many new properties of these functions. These include distortion bounds, sufficiency criteria, extreme points, radius of both starlikness and convexity, weighted mean and partial sum for this newly defined subclass of multivalent functions are discussed. Various integral operators are obtained by putting particular values to the parameters used in the newly defined operator.
Highlights
The study of q-extension of calculus or q-analysis motivated the researchers due to its recent use in different applications
We introduce λ + p −1 the integral operator Jq
We introduce a new integral operator Jq in q-analog and define the class
Summary
The study of q-extension of calculus or q-analysis motivated the researchers due to its recent use in different applications. We have seen applications of q-analysis in Geometric Function Theory (GFT) They were introduced and applied systematically to the generalized q-hypergeometric functions in [3]. Ismail et al [4] used the q-differential operator to examine the geometry of starlike function in q-analog. This theory was later extended to the family of q-starlike function with some order by Agrawal and Sahoo [5]. Due to this development in function theory, many researchers were motivated, as we have seen by Srivastava in [6]. They added significant contributions, which has slowly made this research area more attractive to forthcoming researchers
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