Coefficient estimates for a new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points associated with the Horadam Polynomials

Coefficient estimates for a new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points associated with the Horadam Polynomials

In the present article, we introduce two new subclasses of λ-pseudo biunivalent functions with respect tosymmetrical points in the open unit disk U defined by means of the Horadam polynomials. For functions belonging tothese subclasses , estimates on the Taylor -Maclaurin coefficients ja2j and ja3j are obtained . Fekete–Szegö inequalitiesof functions belonging to these subclasses are also founded. Furthermore, we point out several new special cases of ourresults.

___

  • [1] Alamoush AG, Darus M. Coefficient bounds for new subclasses of bi-univalent functions using Hadamard product. Acta Universitatis Apulensis 2014; 153-161.
  • [2] Alamoush AG, Darus M. Coefficients estimates for bi-univalent of fox-wright functions. Far East Journal of Mathematical Sciences 2014; 249-262.
  • [3] Alamoush AG, Darus M. On coefficient estimates for new generalized subclasses of bi-univalent functions. AIP Conference Proceedings 1614 2014; 844.
  • [4] Altinkaya Ş, Yalçin S. Coefficient estimates for two new subclasses of bi univalent functions with respect to symmetric points. Journal of Function Spaces 2015; Article ID 145242.
  • [5] Babalola KO. On λ-pseudo-starlike functions. Journal of Classical Analysis 2013; 137-147.
  • [6] Brannan DA, Taha TS. On some classes of bi-unvalent functions. In: Mazhar SM, Hamoui A, Faour NS (editors). Mathematical Analysis and its Applications (Kuwait; February 18–21, 1985) , 53–-60, KFAS Proceedings Series, Vol. 3, Pergamon Press (Elsevier Science Limited), Oxford, (1988),see also Studia Universitatis Babeș-Bolyai Mathematica 1986; 70-77.
  • [7] Eker SS, Şeker B. On λ-pseudo bi-starlike and λ-pseudo bi-convex functions with respect to symmetrical points. Tbilisi Mathematical Journal 2018; 49-57.
  • [8] Horadam AF. Jacobsthal Representation Polynomials. The Fibonacci Quarterly 1997; 137-148.
  • [9] Horadam AF, Mahon JM. Pell and Pell-Lucas Polynomials. The Fibonacci Quarterly 1985; 7-20.
  • [10] Horcum T, Kocer EG. On some properties of Horadam polynomials. International Mathematical Forum 2009; 1243-1252.
  • [11] Koshy T. Fibonacci and Lucas Numbers with Applications. A Wiley- Interscience Publication, 2001.
  • [12] Lewin M. On a coefficient problem for bi-univalent functions. Proceeding of the Amarican Mathematical Society 1967; 63-68.
  • [13] Lupas A. A Guide of Fibonacci and Lucas polynomials. Mathematics Magazine 1999; 2-12.
  • [14] Ma WC, Minda D. A unified treatment of some special classes of univalent functions. In: Proceedings of the Conference on Complex Analysis (Nankai Institute of Mathematics 1992); 157-169.
  • [15] Ravichandran V. Starlike and convex functions with respect to conjugate points. Acta Mathematica: Academiae Paedagogicae Nyiregyhaziensis 2004; 31-37.
  • [16] Sakaguchi K. On a certain univalent mapping. The Journal of the Mathematical Society of Japan 1959; 72-75.
  • [17] Srivastava H M, Mishra AK, Gochhayat P. Certain subclasses of analytic and bi-univalent function. Applied Mathematics Letters 2010; 1188-1192.
  • [18] Wang G, Gao CY, Yuan SM. On certain subclasses of close-to-convex and quasi-convex functions with respect to k−symmetric points. Journal of Mathematical Analysis and Applications 2006; 97-106.