New Integral Operator for Analytic Functions

Authors:
Open Access
Publisher website
Google Scholar
Abstract
Let A p n be the class of functions f z given by f z = z p + a p + n z p + n + a p + n + 1 z p + n + 1 + ⋯ which are analytic in the open unit disk U . For f z ∈ A p n , new integral operators O − j f z and O j f z j = 0 , 1 , 2 , ⋯ . are considered. The operators O − j f z and O j f z satisfy O j O − j f z = O − j O j f z = f z and O − j ∗ O j f z = O j ∗ O − j f z = f ∗ f z for the convolution ∗ of O − j f z and O j f z . In the present paper, the dominants for both operators O − j f z and O j f z and subordinations for O − j f z and O j f z are discussed. Also, new subclass T p γ m , δ , ρ ; m , j concerning with m different boundary points is defined and discussed. Moreover, some interesting problems of T p γ m , δ , ρ ; m , j associated with O j f z are obtained. Furthermore, some interesting examples for our results are considered.

This publication has 24 references indexed in Scilit: