The Fekete-Szeg"o Problem for A Generalized Subclass of An-alytic Functions
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In this present work, the authors obtain Fekete-Szego inequality for certain normalized analytic function f(z) defined on the open unit disk for which (1-α)z(Dλ,μmf(z))'+αz(Dλ,μm+1f(z))'/(1-α)Dλ,μmf(z))+αDDλ,μm+1f(z) (λ≥μ≥0,m∈No,α≥0) 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 Hadamard product (or convolution)are given. As a special case of this result, Fekete-Szego inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to generalize the Fekete-Szego inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator Dλ,μm
Abstract
In this present work, the authors obtain Fekete-Szego inequality for certain normalized analytic function f(z) defined on the open unit disk for which (1-α)z(Dλ,μmf(z))'+αz(Dλ,μm+1f(z))'/(1-α)Dλ,μmf(z))+αDDλ,μm+1f(z) (λ≥μ≥0,m∈No,α≥0) 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 Hadamard product (or convolution)are given. As a special case of this result, Fekete-Szego inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to generalize the Fekete-Szego inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator Dλ,μm
참고문헌 (11)
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