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New Subclasses of Harmonic Starlike and Convex Functions

Saurabh Porwal|Kaushal Kishore Dixit
경북대학교 자연과학대학 수학과|2013.09|Kyungpook Mathematical Journal|제53권 제3호|pp. 467-478

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참고문헌

키워드

univalentanalyticHarmonicstarlike and convex functions
주제분류수학

초록

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes VH(β) and UH(β). Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

Abstract

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes VH(β) and UH(β). Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

참고문헌 (17)

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  11. Saurabh Porwal, "An application of certain convolution operator involving hypergeometric functions", J. Raj. Acad. Phy. Sci., 9(2), pp.173~186 (2010)
  12. Saurabh Porwal, "Vinod Kumar and Poonam Dixit, On a subclass of analytic functions defined by convolution", General Mathematics, 19(3), pp.57~65 (2011)
  13. H. Silverman, "Univalent functions with negative coefficients", Proc. Amer. Math. Soc., 51, pp.109~116 (1975)
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  17. B. A. Uralegaddi, "Close-to-Convex functions with positive coefficients", Studia Univ. Babes-Balyai, Mathematica, XL4, pp.25~31 (1995)

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