A Study on Certain Subclasses of Univalent and P Valent Functions Associated with Trigonometric Functions and Some Distribution Series

Abstract

This work is devoted to discuss A study on certain subclasses of univalent and newlinep-valent functions associated with trigonometric functions and some distribution series . newlineOur main objective is to study the new subclasses of starlike and convex functions newlineassociated with cosine function and the estimation of coefficients bounds, Zalcman newlinefunctional, logarathimic coefficients and module difference for the initial consecutive newlinecoefficients. Further, the association with trigonometric functions of and#945; -convex functions is newlinestudied. In particular, we introduce the new subclassess of and#945; -convex functions related to newlinesine and cosine function. This work is continued to obtain the initial coefficients bounds, newlineFekete-Szegand#733;o inequality and Zalcman functional estimate for the same classes. newlineAnd, we find some coefficient estimates, distortion bounds, inclusion and newlineneighborhood results on the subclasses of p-valent functions related to fractional calculus newlineoperator. Further, closure and integral theorems are investigated for finitely many newlinefixed coefficients by using Salagean differential operator. The study continues with the newlinesubclasses of univalent functions associated with some distribution series such as Pascal, newlineMittag Leffer-type Poisson and Generalized distribution. Uniformly Convex Spiralike newlinefunction is given special attention and their association with Poisson distribution series newlineis defined and explored. Finally, the inclusion properties of the subclasses are studied newline