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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 Pureand 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 UniversitatiiOradea, Fasc. Matematica, Tom XVIII, 2011, 5–18.
  • [7] Murugusundaramoorthy G. and Raina R. K., On a subclass of harmonic functions associated with the Wright’s generalizedhypergeometric functions, Hacet. J. Math. Stat., 2009, 28(2), 129–136.
  • [8] Sharma P., Some Wgh inequalities for univalent harmonic analytic functions, Appl. Math, 2010, 464–469.[Crossref]
  • [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 univalentfunctions, 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.
  • [13] Silverman H. and Silvia E. M., Subclasses of harmonic univalent functions, New Zealand J. Math., 1999, 28, 275–284.
  • [14] Ahuja O. P. and Jahangiri J. M., Noshiro-Type harmonic univalent functions, Sci. Math. Jpn., 2002, 6(2), 253–259.
  • [15] Yalcin S.,Ozturk M. and Yamankaradeniz M., A subclass of harmonic univalent functions with negative coefficients, Appl. Math.Comput., 2003, 142, 469-–476.[WoS]
  • [16] AL-Khal R. A. and AL-Kharsani H.A., Harmonic hypergeometric functions, Tamkang J. Math., 2006, 37(3), 273–283.
  • [17] Yalcin S. and Ozturk M., A new subclass of complex harmonic functions, Math. Inequal. Appl., 2004, 7(1), 55–61.
  • [18] Chandrashekar R., Lee S. K. and Subramanian K. G., Hyergeometric functions and subclasses of harmonic mappings,Proceeding of the International Conference on mathematical Analysis 2010, Bangkok, 2010, 95–103.
  • [19] Dixit R. K.K., Pathak A. L., Powal S. and Agarwal R., On a subclass of harmonic univalent functions defined by convolution andintegral 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-Srivastavaoperators, 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]
  • [22] Al-Khal R. A. and AL-Kharsani H. A., Harmonic univalent functions, J. Inequal. Pure Appl. Math., 2007, 8(2), 1–8.
  • [23] Nagpal S. and Ravichandran V., Univalence and convexity in one direction of the convolution of harmonic mappings, Complex Var.Elliptic Equ., 2014, 59(7), 1328–1341.[WoS]
  • [24] Ponnusamy S.,Rasila A. and Kaliraj A., Harmonic close-to-convex functions and minimal surfaces, Complex Var. Elliptic Equ.,2014, 59(9), 986–1002.
  • [25] Porwal S. and Dixit K. K., An application of hypergeometric functions on harmonic univalent functions, Bull. Math. Anal. Appl.,2010, 2(4), 97–105.
  • [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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