GENERALIZED INTEGRAL OPERATORS RELATED WITH p-VALENT ANALYTIC FUNCTIONS

摘要

Let A (P), P is an element of N, be the class of functions f : f (z) = z(P) + Sigma(infinity)(k=1) a(p+k)(zpk), analytic in the unit disc E. For n is an element of N-0, n > -p, an integral operator 1(n+p-1) : A(p) -> A(p) is defined as l(n+p-1)f = f(n+P-1)((-1)) *f such that (f(n+p-1)((-1)) *f(n+P-1)) (z) = z(p)/(1-z)(p+1) where (f(n+p-1)(z) = z(p)/(1-z)(n+p) and * denotes convolution. Using this integral operator, some new classes H-n,H-p(k,alpha,beta,mu,lambda) of A(p) are introduced and certain interesting properties of these classes are studied. A radius problem is also discussed.