Meromorphic multivalent functions associated with Mittage-Leffler Function based on convolution product
Subject Areas : Statistics
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Keywords: Hadamard product (or convolution), extreme point, meromorphic functions, Mittag-Leffler function, estimation of coefficient.,
Abstract :
The Mittag-Leffler function was introduced by Mittag-Leffler, in connection with his method of summation of some divergent series. During the various developments of fractional calculus in the last four decades this function has gained importance and popularity on account of its vast applications in different areas of modern science. This function so occurs in the solution of certain boundary value problems involving fractional integro-differential equations of Volterra type. Mittag-Leffler function is considerably increased among engineers and scientists due to their vast potential of applications in solving the applied problems, such as fluid flow, biological, diffusive transport akin to diffusion, electric networks, probability, and statistical distribution theory. This study defines a new linear operator via the Hadamard product between a meromorphic function and generalized Mittag–Leffler function. The application of the linear operator generates a new subclass of meromorphic function. Also some geometric results related to meromorphic functions such as Hadamard product (or convolution) of functions, integral representation, estimation of coefficient, extreme points of operator are evaluated for this subclass in connection with Mittag-Leffler functions.
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