Certain Subclasses of Multivalent Functions Defined by New Multiplier Transformations

The new multiplier transformations J(p)(delta)(lambda, mu, l) (delta, l >= 0, lambda >= mu >= 0; p is an element of N) of multivalent functions are defined. Making use of the operator J(p)(delta)(lambda, mu, l), two new subclasses P-lambda,mu,l(delta)(A, B; sigma, p) and (P) over tilde (delta)(lambda,mu,l)(A, B; sigma, p) of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, and partial sums, and some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses P-lambda,mu,l(delta)(A, B; sigma, p) and (P) over tilde (delta)(lambda,mu,l)(A, B; sigma, p) are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.