On some differential sandwich theorems using an extended generalized S˘al˘agean operator and extended Ruscheweyh operator

Abstract

Abstract: In this work we define a new operator using the extended generalized Sălăgean operator and extended Ruscheweyh operator. Denote by DR λ the Hadamard product of the extended generalized Sălăgean operator D λ and extended Ruscheweyh operator R , given by DR λ : A ∗ ζ → A ∗ ζ , DR m,n λ f (z, ζ) = (D m λ ∗R ) f (z, ζ) and A∗nζ = {f ∈ H(U ×U), f(z, ζ) = z+an+1 (ζ) z + . . . , z ∈ U, ζ ∈ U} is the class of normalized analytic functions with A∗1ζ = A ∗ ζ . The purpose of this paper is to introduce sufficient conditions for strong differential subordination and strong differential superordination involving the operator DR m,n λ and also to obtain sandwich-type results.