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2011•International Journal of Mathematical ArchiveRequires access

• A NEW CLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH GENERALIZED-DERIVATIVE OPERATOR

A. L. Pathak, K. K. Dixit, R. Agarwal

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Abstract

In this paper, we study a new class of harmonic univalent functions associated with modified generalized – derivative operator in the open unit disk. We obtain numerous sharp results including coefficient conditions, extreme points, distortion bounds, convolution properties and convex combinations for the above class of harmonic univalent functions. The results obtained for the class reduce to the corresponding results for various well-known classes in the literature.

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What this paper is about

In this paper, we study a new class of harmonic univalent functions associated with modified generalized – derivative operator in the open unit disk. We obtain numerous sharp results including coefficient conditions, extreme points, distortion bounds, convolution properties and convex combinations for the above class of harmonic univalent functions. The results obtained for the class reduce to the corresponding results for various well-known classes in the literature.

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Available abstract

In this paper, we study a new class of harmonic univalent functions associated with modified generalized – derivative operator in the open unit disk. We obtain numerous sharp results including coefficient conditions, extreme points, distortion bounds, convolution properties and convex combinations for the above class of harmonic univalent functions. The results obtained for the class reduce to the corresponding results for various well-known classes in the literature.

Key concepts: Extreme point, Mathematics, Convolution (computer science), Class (philosophy), Operator (biology), Harmonic, Distortion (music), Harmonic function

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