In this paper, we discuss and introduce a new study using an integral operator wk,μm in geometric function theory, especially sandwich theorems. We obtained some conclusions for differential subordination superordination formula generalized operator. addition, certain theorems were found. The theory’s features outcomes are symmetric to those derived the theory.

Sanford S. Miller and Petru T. Mocanu’s theory of second-order differential subordinations was extended for the case third-order by José A. Antonino in 2011. In this paper, new results are proved regarding that extend ones involving classical subordination theory. A method finding a dominant is provided when behavior function not known on boundary unit disc. Additionally, obtaining best present...

By making use of the generalized differential operator, the authors derive the subordination and superordination results for certain normalized analytic functions in the open unit disk. Many of the well-known and new results are shown to follow as special cases of our results. 1 Preliminaries Let H be the class of functions analytic in the open unit disc U = {z : | z |< 1}. Let H(a, n) be the s...

Abstract In the present paper, we apply theory of differential subordination to extend famous Jack lemma for analytic functions. Also, using this extension will produce new versions open-door functions, and utilizing them some simple conditions starlikeness meromorphic functions are obtained. Our results improve earlier investigated in literature.

The current study is fully devoted to studying differential subordination and superordination theorems of analytic functions with some sandwich results involving linear operators Iλs,a,μ. This operator was obtained by the Hadamard product family integral Hurwitlz-Lerch Zeta function. demonstrate possibility capability extracting Sandwich theorem, conclusion includes superordination.

For r > 0 let r {z ∈ : |z| < r}. Let 1 . Let the functions f and F be analytic in the unit disc . A function f is called subordinate to F, written f ≺ F, if F is univalent in , f 0 F 0 and f ⊂ F . Let D be a domain in 2 and ψ : 2 ⊃ D → be an analytic function, and let p be a function analytic in with p z , zp′ z ∈ D, z ∈ and h be a function analytic and univalent in . The function p is said to ...