On sandwich theorems for some classes of analytic functions

Abstract

The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Subordination and superordination properties of multivalent functions defined by certain integral operator

“…Lemma 2.2 (Shanmugam et al [15]). Let m; g 2 C with ga0, and let q be a convex function in U with Re 1 þ zq 00 ðzÞ q 0 ðzÞ 4max 0; ÀRe m g ; z 2 U:…”

“…Very recently, Shanmugam et al [14][15][16] obtained the such called sandwich results for certain classes of analytic functions. Further subordination results can be found in [10][11][12][17][18][19]].…”

A Criterion for Bounded Functions

“…Therefore, Theorem 2.5 is a new extension of Theorem A. For another generalization of Theorem A in this direction we refer to [5, p. 70] and to [1], [10]. For φ(z) = 1/(βz + γ) Theorem 2.5 becomes the following corollary, with the Briot-Bouquet differential subordination, for related result we refer to [5, p. 81].…”

Subordination and superordination results for the family of Jung-Kim-Srivastava integral operators

“…Several subordination and superordination results involving this family of integral operators are also derived. For some other recent sandwich-type results in analytic function theory, one can find in [1,2,3,5,6,7,8,9,16,17,18,19,20,22] and the references cited therein.…”