Differential subordination and superordination for certain subclasses of p-valent functions

Abstract

In this paper some subordination and superordination results for higher-order derivatives of certain p-valent analytic functions in the open unit disc are derived. Relevant connections of the results, which are obtained in this paper, with various known results are also considered.

Majorization for certain classes of analytic functions defined by convolution structure

“…where the operator I m, p,q,r,λ (α 1 , β 1 )f (z) was introduced and studied by El-Ashwah and Aouf [6], α 1 , α 2 , ..., α q and β 1 , β 2 , ..., β s are real or complex number (β j ∈ C\Z − 0 = {0, −1, −2, ...} ; j = 1, ..., s; )( q ≤ s + 1; q, s ∈ N 0 , p ∈ N; z ∈ U ) and…”

On differential sandwich theorems of analytic functions defined by certain generalized linear operator

“…where the operator I n,l q,s,λ (a 1 , b 1 )f (z) is introduced and studied by El-Ashwah and Aouf [12].…”

On Sandwich Theorems for Analytic Functions Defined by a Certain Generalized Linear Operator

“…where the operator I n,l q,s,λ (a 1 , b 1 ) was introduced and studied by El-Ashwah and Aouf [12]. In this paper we will derive several subordination results, superordination results and sandwich results involving the operator D n λ,l (f * g) and some of its special chooses of n, l, λ and the function g.…”