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Gangadharan, A.; Shanmugam, T. N.; Srivastava, H. M.

Generalized hypergeometric functions associated with \(k\)-uniformly convex functions. (English) Zbl 1036.33003

Comput. Math. Appl. 44, No. 12, 1515-1526 (2002).
Summary: For a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function, the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as (for example) \(k\)-uniformly convex functions and \(k\)-starlike functions. Relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out.

Cited in 41 Documents

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

Analytic functions; Univalent functions; Generalized hypergeometric functions; Hadamard product (or convolution); Linear operators; \(k\)-starlike functions; Parabolic starlike; functions; Mapping and inclusion properties; Coefficient inequalities; Fractional calculus operators; Gauss summation theorem
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References:

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