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Some properties of generalized convolution of harmonic univalent functions

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Języki publikacji
EN
Abstrakty
EN
The purpose of the present paper is to investigate some interesting properties on generalized convolutions of functions for the classes HP∗(α), HS(α) and HC(α). Further, an application of the convolution on certain integral operator are mentioned.
Wydawca
Rocznik
Strony
63--74
Opis fizyczny
Bibliogr. 38 poz.
Twórcy
autor
  • Department of Mathematics Uiet Campus, CSJM University, Kanpur-208024, (U.P.) India
autor
  • Department of Mathematics Gwalior Institute of Information Technology, Gwalior, (M.P.), India
Bibliografia
  • [1] O. P. Ahuja, Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math. 6(4) (2005), 1–18.
  • [2] Y. Avci, E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect. A (44) (1990), 1–7.
  • [3] R. W. Barnard, CH. Kellog, Applications of convolution operators to problems in univalent function theory, Michigan Math. J. 27 (1980), 81–94.
  • [4] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429–446.
  • [5] B. C. Carlson, D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737–745.
  • [6] J. H. Choi, Y. C. Kim, S. Owa, Generalizations of Hadamard products of functions with negative coefficients, J. Math. Anal. Appl. 199 (1996), 495–501.
  • [7] J. Clunie, T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3–25.
  • [8] H. E. Darwish, On generalizations of Hadamard products of functions with negative coefficients, Proc. Pakistan Acad. Sci. 43(4) (2006), 269–273.
  • [9] H. E. Darwish, M. K. Aouf, Generalizations of modified-Hadamard products of p-valent functions with negative coefficients, Math. Comput. Modelling 49 (2009), 38–45.
  • [10] K. K. Dixit, S. Porwal, On a subclass of harmonic univalent functions, J. Inequal. Pure Appl. Math. 10(1) (2009), 1–18.
  • [11] K. K. Dixit, S. Porwal, A convolution approach on partial sums of certain analytic and univalent functions, J. Inequal. Pure Appl. Math. 10(4) (2009), 1–17.
  • [12] K. K. Dixit, S. Porwal, Some properties of harmonic functions defined by convolution, Kyungpook Math. J. 49(4) (2009), 751–761.
  • [13] T. Domokos, On a subclass of certain starlike functions with negative coefficients, Studia Univ. Babeş-Bolyai Math. (1999), 29–36.
  • [14] P. Duren, Harmonic Mappings in the Plane, Cambridge University Press, (2004).
  • [15] B. A. Frasin, Comprehensive family of harmonic univalent functions, SUT J. Math. 42(1) (2006), 145–155.
  • [16] S. P. Goyal, P. Goswami, N. E. Cho, Argument estimates for certain analytic functions associated with the convolution structure, J. Inequal. Pure Appl. Math. 10(1) (2009), 1–13.
  • [17] J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), 470–477.
  • [18] O. P. Juneja, T. R. Reddy, M. L. Mogra, A convolution approach for analytic functions with negative coefficients, Soochow J. Math. 11 (1985), 69–81.
  • [19] S. Y. Karpuzoˇgullari, M. Öztürk, M. Yamankaradeniz, A subclass of harmonic univalent functions with negative coefficients, Appl. Math. Comput. 142 (2003), 469–476.
  • [20] R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755–758.
  • [21] A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), 352–357
  • [22] J. Nishiwaki, S. Owa, An application of Hölder’s inequality for convolutions, J. Inequal. Pure Appl. Math. 10(4) (2009), 1–14.
  • [23] J. Nishiwaki, S. Owa, H. M. Srivastava, Convolution and Hölder type inequalities for a certain class of analytic functions, Math. Inequal. Appl. 11 (2008), 717–727.
  • [24] K. I. Noor, Convolution techniques for certain classes of analytic functions, Panamer. Math. J. 2(3) (1992), 73–82.
  • [25] S. Owa, The Quasi-Hadamard products of certain analytic functions, in: H. M. Srivastava, S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London, Hong Kong, (1992), 234–251.
  • [26] S. Owa, H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057–1077.
  • [27] M. Öztürk, S. Yalcin, On univalent harmonic functions, J. Inequal. Pure Appl. Math. 3(4) (2002), 1–8.
  • [28] S. Ponnusamy, A. Rasila, Planar harmonic mappings, Ramanujan Mathematical Society Mathematics Newsletters 17(2) (2007), 40–57.
  • [29] S. Ponnusamy, A. Rasila, Planar harmonic and quasi-conformal mappings, Ramanujan Mathematical Society Mathematics Newsletters 17(3) (2007), 85–101.
  • [30] R. K. Raina, D. Bansal, Some properties of a new class of analytic functions defined in terms of a Hadamard product, J. Inequal. Pure Appl. Math. 9(1) (2008), 1–20.
  • [31] M. S. Robertson, On the theory of univalent functions, Ann. of Math. 37 (1936), 374–408.
  • [32] S. Ruscheweyh, Convolutions in Geometric Function Theory, Sem. Math. Sup., Presses Univ. de Montreal, (1982).
  • [33] A. Schild, H. Silverman, Convolution of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Sklodowska Sect. A 29 (1975), 99–107.
  • [34] H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl. 220 (1998), 283–289.
  • [35] H. Silverman, E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math. 28 (1999), 275–284.
  • [36] R. Singh, S. Singh, Convolution properties of a class of starlike functions, Proc. Amer. Math. Soc. 106(1) (1989), 145–152.
  • [37] J. Stankiewicz, Z. Stankiewicz, Some applications of the Hadamard convolution in the theory of functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A 40 (1986), 251–265.
  • [38] H. M. Srivastava, S. Owa, S. K. Chatterjea, A note on certain classes of starlike functions, Rend. Sem. Mat. Univ. Padova 77 (1987), 115–124.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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