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Applications of convolution properties

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EN
Abstrakty
EN
K. I. Noor (2007 Appl. Math. Comput. 188, 814–823) has defined the classes Qk(a, b, λ, γ) and Tk(a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes.
Wydawca
Rocznik
Strony
513--523
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Department of Mathematics, Rzeszów University of Technology, Wincentego Pola 2, 35-959 Rzeszów, Poland
Bibliografia
  • [1] B. C. Carlson, D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737–745.
  • [2] J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432–445.
  • [3] J. Dziok, On the convex combination of the Dziok–Srivastava operator, Appl. Math. Comput. 188 (2007), 1214–1220.
  • [4] J. Dziok, On some applications of the Briot–Bouquet differential subordinations, J. Math. Anal. Appl. 328 (2007), 295–301.
  • [5] J. Dziok, H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1–13.
  • [6] D. J. Hallenbeck, T. H. MacGregor, Linear Problems and Convexity Technics in Geometric Function Theory, Pitman Publ. Ltd., London, 1984.
  • [7] Y. Ling, F. Liu, G. Bao, Some properties of an integral transforms, Appl. Math. Lett. 19 (2006), 830–833.
  • [8] J.-L. Liu, H. M. Srivastava, Classes of meromorphically multivalent functions associated with the generalized hypergeometric function, Math. Comput. Modelling 39 (2004), 21–34.
  • [9] J.-L. Liu, H. M. Srivastava, Certain properties of the Dziok–Srivastava operator, Appl. Math. Comput. 159 (2004), 485–493.
  • [10] C. Loewner, Untersuchungen über die Verzerrung bei konformen Abbildungen des Einheitskreises z < 1, die durch Funktionen mit nicht verschwindender Ableitung geliefert werde, Ber. Vehr. Sächs. Ges. Wiss. Leipzig 69 (1917), 89–106.
  • [11] S. S. Miller, P. T. Mocanu, Differential Subordinations: Theory and Applications, Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York, 2000.
  • [12] K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 (2006), 1872–1881.
  • [13] K. I. Noor, On some applications of certain integral operators, Appl. Math. Comput. 188 (2007), 814–823.
  • [14] V. Paatero, Über die konforme Abbildung von Gebieten deren Ränder von beschränkter Drehung sind., Ann. Acad. Sci. Fenn. Ser. A 33(9) (1931), 77 pp.
  • [15] V. Paatero, Über Gebiete von beschränkter Randdrehung, Ann. Acad. Sci. Fenn. Ser. A 37(9) (1933), 20 pp.
  • [16] K. S. Padmanabhan, R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31 (1975), 311–323.
  • [17] J. Patel, A. K. Mishra, H. M. Srivastava, Classes of multivalent analytic functions involving the Dziok–Srivastava operator, Comput. Math. Appl. 54(2007), 599–616.
  • [18] K. Piejko, J. Sokół, On the Dziok–Srivastava operator under multivalent analytic functions, Appl. Math. Comput. 177(2006), 839–843.
  • [19] B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math. 10 (1971), 7–16.
  • [20] C. Ramachandran, T. N. Shanmugam, H. M. Srivastava, A unified class of k-uniformly convex functions defined by the Dziok–Srivastava linear operator, Appl. Math. Comput. 190 (2007), 1627–1636.
  • [21] St. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de l’Univ. de Montreal, 1982.
  • [22] H. M. Srivastava, N-Eng-Xu, Ding-Gong Yang, Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives, J. Math. Anal. Appl. 331 (2007), 686–700.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f31c28d2-144c-4e2c-805f-9af10be28bbc
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