WHITTAKER'S EQUATION-BASED FORMULATION OF A NEW CLASS OF ANALYTIC FUNCTIONS COMBINED WITH GEOMETRIC ANALYSIS

WHITTAKER'S EQUATION-BASED FORMULATION OF A NEW CLASS OF ANALYTIC FUNCTIONS COMBINED WITH GEOMETRIC ANALYSIS

R. W. Ibrahim

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Abstract

A special function is a function with a particular use in mathematical physics or another branch of mathematics and is often named after an early scientist who researched its characteristics. A few noteworthy instances exist, such as the hypergeometric function and its distinct species. By using k-calculus, this sort of special function is made more generic. K-symbol calculus is utilized in this study to develop the k-convoluted operators associated with the k-Whittaker function (con uent hypergeometric function of the  rst kind). Through the use of this recently created operator, we propose a new geometric formula of normalized functions in the unit disk. Our strategy is to modify the theory of di erential subordination, thus we geometrically investigate the most well-known characteristics of this new operator, including subordination features and coe  cient bounds. We draw attention to some notable corollaries of our main conclusions as exceptional examples.

Keywords

univalent function, fractional calculus, the open unit disk, analytic function, subordination and superordination