Some properties of a generalized multiplier transform on analytic p -valent functions

Abstract

UDC 517.5 For a function f ( z ) = z p + ∑ k = 1 ∞ a k + p z k + p , where p ∈ ℕ , the authors investigate some properties of a more general multiplier transform on analytic p -valent functions in an open unit disk. The applications of the obtained results to fractional calculus are pointed out, while several other corollaries follow as simple consequences.

Some Results on Various Subclasses of Harmonic P-valent Functions Associated With Pascal Distribution Series

“…Suppose that γ represent the class of all analytic functions f(z), having the series notation Further, let S denote the class of all Normalized Analytic Functions that are univalent in E. (see [5], [8]). Also, let Ω represent the set of all complex valued harmonic p-valent functions of the form fp = hp + g p defined in the open unit disk E = {z : |z| < 1}, such that…”