On Generalized Integral Operator Based on Salagean Operator
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Let A(p) be the class of function f: z^{p} + sum^{infty }_{j=1} a_{j} z^{p+j} analytic in the open unit disc E. Let, for any integer n > -p, f_{n+p-1} (z) = z^{p} + sum^{infty}_{j=1} (p+j)^{n+p-1} z^{p+j}. We define f^{(-1)}_{n+p-1}(z) by using convolution as f_{n+p-1} * f^{-1}_{n+p-1} = {z^{p}/{(1-z)^{n+p}}. A function p, analytic in E with p(0) = 1, is in the class P_{k} if int^{2pi }_{0} {Re }p(z)-{p} dthetal kpi, where z = re^{itheta}. We use the class P_{k} to introduce a new class of multivalent analytic functions and define an integral operator L_{n+p-1} (f) = f^{-1}_{n+p-1}* f for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.
Abstract
Let A(p) be the class of function f: z^{p} + sum^{infty }_{j=1} a_{j} z^{p+j} analytic in the open unit disc E. Let, for any integer n > -p, f_{n+p-1} (z) = z^{p} + sum^{infty}_{j=1} (p+j)^{n+p-1} z^{p+j}. We define f^{(-1)}_{n+p-1}(z) by using convolution as f_{n+p-1} * f^{-1}_{n+p-1} = {z^{p}/{(1-z)^{n+p}}. A function p, analytic in E with p(0) = 1, is in the class P_{k} if int^{2pi }_{0} {Re }p(z)-{p} dthetal kpi, where z = re^{itheta}. We use the class P_{k} to introduce a new class of multivalent analytic functions and define an integral operator L_{n+p-1} (f) = f^{-1}_{n+p-1}* f for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.
참고문헌 (7)
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