Abstract
Here, we study strong differential subordinations for the extended new operator IRλ,lm defined by the Hadamard product of the extended multiplier transformation Im,λ,l and the extended Ruscheweyh derivative Rm, on the class of normalized analytic functions Anζ∗={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}, by IRλ,lm:Anζ∗→Anζ∗, IRλ,lmfz,ζ=Im,λ,l∗Rmfz,ζ.
Highlights
Different types of operators have been used from early on in the study of complex functions
Here, we study strong differential subordinations for the extended new operator IRmλ,l defined by the Hadamard product of the extended multiplier transformation I(m, λ, l) and the extended Ruscheweyh derivative Rm, on the class of normalized analytic functions A∗nζ = { f ∈ H(U × U), f (z, ζ) = z + an+1(ζ)zn+1 + . . . , z ∈ U, ζ ∈ U}, by IRmλ,l : A∗nζ → A∗nζ, IRmλ,l f (z, ζ) = (I(m, λ, l) ∗ Rm) f (z, ζ)
Generalizing the concept of differential subordination and using the operator defined by using the multiplier transformation and Ruscheweyh operator, further study is carried out and new strong subordinations are obtained, giving their best dominant
Summary
Different types of operators have been used from early on in the study of complex functions. Abstract: Here, we study strong differential subordinations for the extended new operator IRmλ,l defined by the Hadamard product of the extended multiplier transformation I(m, λ, l) and the extended Ruscheweyh derivative Rm, on the class of normalized analytic functions A∗nζ = { f ∈ H(U × U), f (z, ζ) = z + an+1(ζ)zn+1 + . In studying the strong differential subordinations, we will use the following lemmas.
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