Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2016: 0.346
5-year IMPACT FACTOR: 0.412

CiteScore 2016: 0.42

SCImago Journal Rank (SJR) 2016: 0.489
Source Normalized Impact per Paper (SNIP) 2016: 0.745

Mathematical Citation Quotient (MCQ) 2016: 0.24

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 64, Issue 6

Issues

Neighbourhoods of two new classes of harmonic univalent functions with varying arguments

Elif Yaşar / Sibel Yalçin
Published Online: 2015-01-10 | DOI: https://doi.org/10.2478/s12175-014-0283-x

Abstract

In this paper, two new classes of harmonic univalent functions with varying arguments are defined by using planar harmonic convolution operator involving hypergeometric functions. Those classes are of special interest because they contain various classes of well-known harmonic univalent functions such as the classes of k-starlike and k-uniformly convex harmonic univalent functions. The main purpose of this paper is to investigate neighbourhoods of the classes in question.

MSC: Primary 30C45,30C50; Secondary 33C05

Keywords: harmonic; k-starlike; k-uniformly convex; hypergeometric functions; varying arguments; convolution; neighbourhood

  • [1] AHUJA, O. P.— AGHALARY, R.— JOSHI, S. B.: Harmonic univalent functions associated with k-uniformly starlike functions, Math. Sci. Res. J. 9 (2005), 9–17. Google Scholar

  • [2] AHUJA, O. P.: Planar harmonic convolution operators generated by hypergeometric functions, Integral Transforms Spec. Funct. 18 (2007), 165–177. http://dx.doi.org/10.1080/10652460701210227Web of ScienceCrossrefGoogle Scholar

  • [3] ALI, R. M.— STEPHEN, A.— SUBRAMANIAN, K. G.: Subclasses of harmonic mappings defined by convolution, Appl. Math. Lett. 23(10) (2010), 1243–1247. http://dx.doi.org/10.1016/j.aml.2010.06.006CrossrefWeb of ScienceGoogle Scholar

  • [4] AVCI, Y.— ZLOTKIEWICZ, E.: On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect. A 44 (1990), 1–7. Google Scholar

  • [5] BERNARDZ, U.— KANAS, S.: Generalized neighbourhoods and stability of convolution for the class of k-uniformly convex and k-starlike functions, Folia. Sci. Tech. Rzeszów Math. 175 (1999), 29–38. Google Scholar

  • [6] BERNARDZ, U.— KANAS, S.: Stability of the integral convolution of k-uniformly convex and k-starlike functions, J. Appl. Anal. 10 (2004), 105–115. Google Scholar

  • [7] CARLSON, B. C.— SHAFFER, D. B.: Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737–745. http://dx.doi.org/10.1137/0515057CrossrefGoogle Scholar

  • [8] CHOI, J. H.— SAIGO, M.— SRIVASTAVA, H. M.: Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432–445. http://dx.doi.org/10.1016/S0022-247X(02)00500-0CrossrefGoogle Scholar

  • [9] CLUNIE, J.— SHEIL-SMALL, T.: Harmonic univalent functions, Ann. Acad. Sci. Fenn. Math. 9 (1984), 3–25. http://dx.doi.org/10.5186/aasfm.1984.0905CrossrefGoogle Scholar

  • [10] COTIRLA, L. I.: Harmonic univalent functions defined by an integral operator, Acta Univ. Apulensis Math. Inform. 17 (2009), 95–105. Google Scholar

  • [11] DE BRANGES, L.: A proof of the Bierbach conjecture, ActaMath. 154 (1985), 137–152. Google Scholar

  • [12] DZIOK, J.— SRIVASTAVA, H. M.: Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7–18. http://dx.doi.org/10.1080/10652460304543CrossrefGoogle Scholar

  • [13] EL-ASHWAH, R. M.— AOUF, M. K.: New classes of p-valent harmonic functions, Bull. Math. Anal. Appl. 2 (2010), No. 3, 53–64. Google Scholar

  • [14] GOODMAN, A. W.: Univalent functions and non-analytic curves, Proc. Amer. Math. Soc. 8 (1957), 598–601. http://dx.doi.org/10.1090/S0002-9939-1957-0086879-9CrossrefGoogle Scholar

  • [15] GOODMAN, A.W.: On uniformly convex functions, Ann. Polon. Math. 56 (1991), 87–92. Google Scholar

  • [16] HOHLOV, Y. E.: Operators and operations in the class of univalent functions, Izv.Vyssh. Uchebn. Zaved. Mat. 10 (1978), 83–89 (Russian). Google Scholar

  • [17] JAHANGIRI, J. M.: Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), 470–477. http://dx.doi.org/10.1006/jmaa.1999.6377CrossrefGoogle Scholar

  • [18] JAHANGIRI, J. M.— SILVERMAN, H.: Harmonic univalent functions with varying arguments, Int. J. Appl. Math. 8 (2002), 267–275. Google Scholar

  • [19] JAHANGIRI, J. M.— MURUGUSUNDARAMOORTHY, G.— VIJAYA, K.: Salageantype harmonic univalent functions, South. J. Pure Appl. Math. 2 (2002), 77–82. Google Scholar

  • [20] KANAS, S.— WISNIOWSKA, A.: Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), 327–336. http://dx.doi.org/10.1016/S0377-0427(99)00018-7CrossrefGoogle Scholar

  • [21] KANAS, S.: Stability of convolution and dual sets for the class of k-uniformly convex and k-starlike functions, Folia. Sci. Tech. Rzeszów Math.170 (1998), 51–64. Google Scholar

  • [22] KIM, Y. C.— JAHANGIRI, J. M.— CHOI, J. H.: Certain convex harmonic functions, Int. J. Math. Math. Sci. 29 (2002), 459–465. http://dx.doi.org/10.1155/S0161171202007585CrossrefGoogle Scholar

  • [23] MURUGUSUNDARAMOORTHY, G.: A class of Ruscheweyh-type harmonic univalent functions with varying arguments, Southwest J. Pure Appl. Math. 2 (2002), 90–95. Google Scholar

  • [24] OWA, S.: On the distortion theorems I, Kyungpook Math. J. 18 (1978), 53–59. Google Scholar

  • [25] OWA, S.— SRIVASTAVA, H. M.: Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057–1077. http://dx.doi.org/10.4153/CJM-1987-054-3CrossrefGoogle Scholar

  • [26] RONNING, F.: Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), 189–196. http://dx.doi.org/10.1090/S0002-9939-1993-1128729-7CrossrefGoogle Scholar

  • [27] ROSY, T.— STEPHEN, B. A.— SUBRAMANIAN, K. G.: Goodman-Ronning-type harmonic univalent functions, Kyungpook Math. J. 41 (2001), 45–54. Google Scholar

  • [28] RUSCHEWEYH, S.: New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115. http://dx.doi.org/10.1090/S0002-9939-1975-0367176-1CrossrefGoogle Scholar

  • [29] RUSCHEWEYH, S.: Neighbourhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), 521–527. http://dx.doi.org/10.1090/S0002-9939-1981-0601721-6CrossrefGoogle Scholar

  • [30] SILVERMAN, H.: Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl. 220 (1998), 283–289. http://dx.doi.org/10.1006/jmaa.1997.5882CrossrefGoogle Scholar

  • [31] SILVERMAN, H.— SILVIA, E. M.: Subclasses of harmonic univalent functions, N.Z. J. Math. 28 (1999), 275–284. Google Scholar

  • [32] SILVERMAN, H.— MURUGUSUNDARAMOORTHY, G.— VIJAYA, K.: A class of starlike functions defined by the Dziok-Srivastava operator, Kyungpook Math. J. 49 (2009), 95–106. http://dx.doi.org/10.5666/KMJ.2009.49.1.095CrossrefGoogle Scholar

About the article

Published Online: 2015-01-10

Published in Print: 2014-12-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 6, Pages 1409–1420, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-014-0283-x.

Export Citation

© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in