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2015 | 13 | 1 |

Tytuł artykułu

Inequalities of harmonic univalent functions with connections of hypergeometric functions

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.

Wydawca

Czasopismo

Rocznik

Tom

13

Numer

1

Opis fizyczny

Daty

otrzymano
2015-04-01
zaakceptowano
2015-09-16
online
2015-10-21

Twórcy

  • Department of Mathematics, Rzeszów University of Technology, Al. Powsta´nców Warszawy 12, 35-959 Rzeszów,
    Poland
  • Faculty of Computer Science and Information Technology, University Malaya,
    50603 Kuala Lumpur, Malaysia
autor
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau Perlis, Malaysia
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau Perlis, Malaysia

Bibliografia

  • [1] Clunie J. and Sheil-Small T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A. I. Math., 1984, 9, 3–25
  • [2] Ahuja O. P. and Silverman H., Inequalities associating hypergeometric functions with planer harmonic mapping, J. Inequal Pure and Appl. Maths., 2004, 5, 1–10.
  • [3] Ahuja O. P., Planer harmonic convolution operators generated by hypergeometric functions, Trans. Spec. Funct., 2007, 18, 165–177. [Crossref]
  • [4] Ahuja O. P., Connections between various subclasses of planer harmonic mappings involving hypergeometric functions, Appl. Math. Comput, 2008, 198, 305–316. [WoS]
  • [5] Ahuja O. P., Harmonic starlikeness and convexity of integral operators generated by hypergeometric series, Integ. Trans. Spec. Funct., 2009, 20(8), 629–641. [Crossref][WoS]
  • [6] Ahuja O. P., Inclusion theorems involving uniformly harmonic starlike mappings and hypergeometric functions, Analele Universitatii Oradea, Fasc. Matematica, Tom XVIII, 2011, 5–18.
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  • [9] Raina R. K. and Sharma P., Harmonic univalent functions associated with Wright’s generalized hypergeometric functions, Integ. Trans. Spec. Funct., 2011, 22(8), 561–572. [Crossref][WoS]
  • [10] Ahuja O. P. and Sharma P., Inclusion theorems involving Wright’s generalized hypergeometric functions and harmonic univalent functions, Acta Univ. Apulensis, 2012, 32, 111–128.
  • [11] Avci Y. and Zlotkiewicz E., On harmonic univalent mappings, Ann. Univ. Marie Curie-Sklodowska Sect. A, 1991, 44, 1–7.
  • [12] Silverman H., Harmonic univalent functions with negative coefficients, J. Math. Anal. Apl., 1998, 220, 283–289.
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  • [19] Dixit R. K.K., Pathak A. L., Powal S. and Agarwal R., On a subclass of harmonic univalent functions defined by convolution and integral convolution, I. J. Pure Appl. Math., 2011, 69(3), 255–264.
  • [20] Aouf M.K., Mostafa A. O., Shamandy A. and Adwan E. A., Subclass of harmonic univalent functions defined by Dziok-Srivastava operators, Le Math., 2013, LXVIII, 165–177.
  • [21] El-Ashwah R.M., Subclass of univalent harmonic functions defined by dual convolution, J. Inequal. Appl., 2013, 2013:537, 1–10. [Crossref][WoS]
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  • [26] Shelake G., Joshi S., Halim S., On a subclass of harmonic univalent functions defined by convolution, Acta Univ. Apulensis, 2014, 38, 251–262.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_1515_math-2015-0066
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