SOME RESULTS ON ANALYTIC FUNCTIONS ASSOCIATED WITH VERTICAL STRIP DOMAIN
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For real parameters α and β such that α < 1 < β, we denote by Ρ(α, β) the class of analytic functions p, which satisfy p(0) = 1 and the following two-sided inequality: α < R｛p(z)｝ < β (z ∈ D), where D denotes the open unit disk. We denote by S*(α, β), K(α, β), M(α, β) and N(α, β) the classes of normalized analytic functions f, which satisfy that each function zf'(z)/f(z), 1 + (zf"(z)=f'(z)), f'(z) and f(z)/z belongs to the class P(α, β), respectively. In this paper, we βnd some sufficient conditions on functions to be in the class P(α, β). Applying these results, we βnd some inclusion relationships related to the above classes.
Abstract
For real parameters α and β such that α < 1 < β, we denote by Ρ(α, β) the class of analytic functions p, which satisfy p(0) = 1 and the following two-sided inequality: α < R｛p(z)｝ < β (z ∈ D), where D denotes the open unit disk. We denote by S*(α, β), K(α, β), M(α, β) and N(α, β) the classes of normalized analytic functions f, which satisfy that each function zf'(z)/f(z), 1 + (zf"(z)=f'(z)), f'(z) and f(z)/z belongs to the class P(α, β), respectively. In this paper, we βnd some sufficient conditions on functions to be in the class P(α, β). Applying these results, we βnd some inclusion relationships related to the above classes.
참고문헌 (11)
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