Fekete-Szego Problem for a Generalized Subclass of Analytic Functions
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In this present work, the authors obtain Fekete-Szeg¨o inequality for certainnormalized analytic function f(z) defined on the open unit disk for which λβz3(L(a, c)f(z))′′′+ (2λβ +λ-β)z2(L(a, c)f(z))′′+ z(L(a, c)f(z))′/λβz2(L(a, c)f(z))′′+ (λ-β)z(L(a, c)f(z))′ + (1 - λ+β)(L(a, c)f(z)) (0 ≤ ≤ λ ≤ 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamardproduct (or convolution) are given. As a special case of this result, Fekete-Szeg¨o inequalityfor a class of functions defined through fractional derivatives are obtained.
Abstract
In this present work, the authors obtain Fekete-Szeg¨o inequality for certainnormalized analytic function f(z) defined on the open unit disk for which λβz3(L(a, c)f(z))′′′+ (2λβ +λ-β)z2(L(a, c)f(z))′′+ z(L(a, c)f(z))′/λβz2(L(a, c)f(z))′′+ (λ-β)z(L(a, c)f(z))′ + (1 - λ+β)(L(a, c)f(z)) (0 ≤ ≤ λ ≤ 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamardproduct (or convolution) are given. As a special case of this result, Fekete-Szeg¨o inequalityfor a class of functions defined through fractional derivatives are obtained.
참고문헌 (11)
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