THE SUBORDINATION THEOREM FOR γ-µ-SPIRAL-LIKE FUNCTIONS OF ORDER λ

THE SUBORDINATION THEOREM FOR γ-µ-SPIRAL-LIKE FUNCTIONS OF ORDER λ

S. Salehian, A. Motamednezhad

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Abstract

In this paper, we introduce a novel subclass Sγ(λ, μ) of normalized analytic functions in the open unit disk U. First we obtain several sufficient conditions that a function belongs to the subclass Sγ(λ, μ). Furthermore, we derive the upper bounds for the initial Taylor-Maclaurin coefficients |a2|, |a3| and |a4| as well as the Fekete-Szeg¨o type inequalities for functions belong to this subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Keywords

γ-spiral-like functions, γ-spiral-like functions of order λ, Subordination, Hadamard product, Coefficient estimates.