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).
@article{bwmeta1.element.doi-10_2478_aupcsm-2014-0005,
author = {Kaliappan Vijaya and Gangadharan Murugusundaramoorthy and Murugesan Kasthuri},
title = {Starlike functions of complex order involving q-hypergeometric functions with fixed point},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {13},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_aupcsm-2014-0005}
}
Kaliappan Vijaya; Gangadharan Murugusundaramoorthy; Murugesan Kasthuri. Starlike functions of complex order involving q-hypergeometric functions with fixed point. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 13 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_aupcsm-2014-0005/
[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.