The Journal of the Indian Mathematical Society

Abstract

A function g(z) = z +a₂z² + . . . , regular in |z| < 1 is said to be close-to-convex in |z| < 1 if there exists a function G(z) = z +b₂t² + . . . regular and starlike in |z| < 1 and such that

Re {z g'(z)/G(z)}>0 (|z|<1).            (1)

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Abstract

A function/regular in |z| < 1 and normalised so that f(0) = 0, f'(0) = 1 is said to be spiral-like in |z| < 1 if there exists a real number α, | α | < π/2, such that

Re {e^iα f'(z)/f(z)}>0 (|z|<1). (1)

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Abstract

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