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2014 | 13 |
Tytuł artykułu

Starlike functions of complex order involving q-hypergeometric functions with fixed point

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).
Słowa kluczowe
Rocznik
Tom
13
Opis fizyczny
Daty
wydano
2014-12-01
otrzymano
2014-02-27
poprawiono
2014-06-03
online
2014-12-11
Twórcy
  • School of Advanced Sciences VIT University Vellore - 632014 India, kvijaya@vit.ac.in
  • School of Advanced Sciences VIT University Vellore - 632014 India
Bibliografia
  • [1] Md. Aabed, M. Darus, A generalized operator involving the q-hypergeometric function, Mat. Vesnik 65 (2013), no. 4, 454-465. Cited on 52 and 53.
  • [2] O. Altintas, O. Ozkan, H.M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Lett. 13 (2000), no. 3, 63-67. Cited on 53.[Crossref]
  • [3] M.K. Aouf, A. Shamandy, A.O. Mostafa, S. Madian, A subclass of M-W-starlike functions, Univ. Apulensis Math. Inform. No. 21 (2010), 135-142. Cited on 53.
  • [4] S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969) 429-446. Cited on 53.[Crossref]
  • [5] B.C. Carlson, S.B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), no. 4, 737-745. Cited on 53.[Crossref]
  • [6] J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), no. 1, 1-13. Cited on 53.[Crossref]
  • [7] J. Dziok, H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), no. 1, 7-18. Cited on 53.
  • [8] A.W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601. Cited on 52.[Crossref]
  • [9] S. Kanas, F. Rønning, Uniformly starlike and convex functions and other related classes of univalent functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 53 (1999), 95-105. Cited on 52.
  • [10] R.J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965) 755-758. Cited on 52 and 53.[Crossref]
  • [11] R.J. Libera, Univalent -spiral functions, Canad. J. Math. 19 (1967) 449-456.Cited on 54.[Crossref]
  • [12] J.E. Littlewood, On inequalities in theory of functions, Proc. Lond. Math. Soc. 23 (1925), 481-519. Cited on 59.[Crossref]
  • [13] A.E. Livingston, On the radius of univalence of certain analytic functions, Proc.Amer. Math. Soc. 17 (1966) 352-357. Cited on 53.[Crossref]
  • [14] G. Murugusundaramoorthy, H.M. Srivastava, Neighborhoods of certain classes of analytic functions of complex order, JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), no. 2, Article 24, 8 pp. Cited on 53 and 60.
  • [15] S.D. Purohit, R.K. Raina, Certain subclasses of analytic functions associated with fractional q-calculus operators, Math. Scand. 109 (2011), no. 1, 55-70. Cited on52.
  • [16] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115. Cited on 53.[Crossref]
  • [17] S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521-527. Cited on 60.[Crossref]
  • [18] L. Špacek, Príspẽvek, k teorii funkci prostých, Casopis Pest. Math. 63 (1933), 12-19. Cited on 54.
  • [19] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math.Soc. 51 (1975), 109-116. Cited on 52 and 56.[Crossref]
  • [20] H. Silverman, Integral means for univalent functions with negative coefficients, Houston J. Math. 23 (1997), no. 1, 169-174. Cited on 59.
  • [21] H.M. Srivastava, S. Owa, A note on certain subclasses of spiral-like functions, Rend. Sem. Mat. Univ. Padova 80 (1988), 17-24. Cited on 54.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_aupcsm-2014-0005
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