The Journal of the Indian Mathematical Society

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A Note on Spiral-Like Functions


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1 Punjabi University, Patiala, India
     

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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 {eiα f'(z)/f(z)}>0 (|z|<1). (1)


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  • A Note on Spiral-Like Functions

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Authors

Ram Singh
Punjabi University, Patiala, India

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 {eiα f'(z)/f(z)}>0 (|z|<1). (1)