On λ-pseudo q -bi-starlike functions

On λ-pseudo q -bi-starlike functions

Making use of the -pseudo-q -differential operator, we aim to investigate a new, interesting class of bi-starlikefunctions in the conic domain. Furthermore, we obtain certain sharp bounds of the Fekete–Szegö functional for functionsbelonging to this class.

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  • [1] Abdel-Gawad HR, Thomas DK. The Fekete-Szegö coefficient problems for strongly close-to-convex functions. P Am Math Soc 1992; 114: 345-349.
  • [2] Altinkaya Ş, Özkan SY. On Sălăgean type pseudo-starlike functions. Acta et Commentationes Universitatis Tartuensis de Mathematica 2017; 21: 275-285.
  • [3] Babalola KO. On -pseudo starlike functions. J Classical Anal 2013; 2: 137-147.
  • [4] Darus M, Hussain S, Raza M, Sokół J. On a subclass of starlike functions. Result Math 2018; 73: 22.
  • [5] Frasin BA, Auof MK. New subclasses of bi-univalent functions. Appl Math Lett 2011; 24: 1569-1673.
  • [6] Ismail MEH, Merkes E, Styer D. A generalization of starlike functions. Complex Variable Theory Appl 1990; 14: 77-84.
  • [7] Jahangiri JM, Hamidi SG. Coefficient estimates for certain classes of bi-univalent functions. Int J Math Math Sci 2013; 2013: 190560.
  • [8] Joshi SB, Altinkaya Ş, Yalçin S. Coefficient estimates for Sălăgean type bi-pseudo-starlike functions. Kyungpook Mathematical Journal 2017; 57: 613-621.
  • [9] Keogh FR, Merkes EP. A Coefficient inequality for certain classes of analytic functions. P Am Math Soc 1969; 20: 8-12.
  • [10] Kamble PN, Shrigan MG. Initial coefficient estimates for bi-univalent functions. Far East J Math 2018; 102: 271-282.
  • [11] Kamble PN, Shrigan MG, Srivastava HM. A novel subclass of univalent functions involving operators of fractional calculus. Int J Appl Math 2017; 30: 501-514.
  • [12] Kanas S, Răducanu D. Conic regions and k-uniform convexity. J Comput Appl Math 1999; 105: 327-336.
  • [13] Kanas S, Răducanu D. Some subclass of analytic functions related to conic domains. Math Slovaca 2014; 64: 1183-1196.
  • [14] London RR, Thomas DK. The derivative of Bazilevic̆functions. P Am Math Soc 1988; 104: 85-89.
  • [15] Ma W, Minda D. A Unified Treatment of Some Special Classes of Univalent Functions. Cambridge, MA, USA: MIT Press, 1994.
  • [16] Purohit SD, Raina RK. Certain subclasses of analytic functions associated with fractional q-calculus operators. Math Scand 2011; 109: 55-70.
  • [17] Robertson MS. Quasi-subordination and coefficient conjecture. B Am Math Soc 1970; 76: 1-9.
  • [18] Singh R. On Bazilevic̆functions. B Am Math Soc 1973; 38: 261-271.
  • [19] Srivastava HM. Univalent functions, fractional calculus, and associated generalized hypergeometric functions. In: Srivastava HM, Owa S, editors. Univalent Functions, Fractional Calculus, and Their Applications. New York, NY, USA: John Wiley and Sons, 1989, pp. 329-354.
  • [20] Srivastava HM, Altinkaya Ş, Yalçin S. Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator. Filomat 2018; 32: 503-516.
  • [21] Srivastava HM, Bulut S, Çağlar M, Yağmur N. Coefficient estimates for a general subclass of analytic and biunivalent functions. Filomat 2013; 27: 831-842.
  • [22] Srivastava HM, Gaboury S, Ghanim F. Coefficient estimates for some general subclasses of analytic and bi-univalent functions. Afrika Math 2017; 28: 693-706.
  • [23] Srivastava HM, Sümer S, Hamidi SG, Jahangiri JM. Faber polynomial coefficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator. Bull Iranian Math Soc 2017; 44: 149-157.