Some families of linear operators associated with certain subclasses of multivalent functions

Abstract

Making use of a certain linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce two novel subclasses P a , c ( A , B ; p , λ ) and P a , c + ( A , B ; p , λ ) of the class A ( p ) of normalized p -valent analytic functions in the open unit disk. The main objective of the present paper is to investigate the various important properties and characteristics of each of these subclasses. Furthermore, several properties involving neighborhoods of functions in these subclasses are investigated. We also derive many results for the modified Hadamard products of functions belonging to the class P a , c + ( A , B ; p , λ ) . Finally, some applications of fractional calculus operators are considered.