Coefficient bounds for a new family of bi-univalent functions associated with $(U,V)$-Lucas polynomials

The aim of this paper is to use (U,V)-Lucas polynomials to introduce and study a new family of holomorphic and bi-univalent functions defined in the open unit disk which involve q-derivative operator. We investigate upper bounds for the Taylor-Maclaurin coefficients |d2| and |d3| and Fekete- Szego problem for functions belongs to this new family. Some interesting consequences of the results established here are indicated.

[1]  H. Orhan,et al.  Coefficient bounds for new subclasses of bi-univalent functions , 2012, 1204.4285.

[2]  N. Ayırtman,et al.  Univalent Functions , 1965, Series and Products in the Development of Mathematics.

[3]  A. K. Mishra,et al.  The fekete-szegö-problem for a subclass of close-to-convex functions , 2001 .

[4]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[5]  Ussain,et al.  The Fekete-Szegö functional for a subclass of analytic functions associated with quasi-subordination , 2018 .

[6]  S. Yalçın,et al.  On the (p, q)-Lucas polynomial coefficient bounds of the bi-univalent function class $$\sigma $$σ , 2018, Boletín de la Sociedad Matemática Mexicana.

[7]  Gwang Yeon Lee,et al.  Some Properties of the (p, q)-Fibonacci and (p, q)-Lucas Polynomials , 2012, J. Appl. Math..

[8]  A. Bersani,et al.  The class of Lucas-Lehmer polynomials , 2016, 1603.01989.

[9]  Arzu Özkoç,et al.  A NOTE FOR THE $(p,q)-$FIBONACCI AND LUCAS QUATERNION POLYNOMIALS , 2017 .

[10]  B. Alkahtani,et al.  Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions , 2015, 1503.04644.

[11]  Hari M. Srivastava,et al.  Certain subclasses of analytic and bi-univalent functions , 2010, Appl. Math. Lett..

[12]  Piero Filipponi,et al.  Derivative Sequences of Fibonacci and Lucas Polynomials , 1991 .

[13]  Bulut Serap.  Certain subclasses of analytic and bi-univalent functions involving the q-derivative operator , 2017 .

[14]  H. Srivastava,et al.  Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions , 2015 .

[15]  F. Sakar,et al.  Coefficient Estimates for Certain Subclasses of m-fold Symmetric Bi-univalent Functions Defined by the Q-derivative Operator , 2018 .

[16]  Hari M. Srivastava,et al.  Some applications of a subordination theorem for a class of analytic functions , 2008, Appl. Math. Lett..

[17]  K. O. Babalola.  On λ-pseudo-starlike functions , 2013 .

[18]  H. Srivastava,et al.  Certain Subclasses of Bi-Univalent Functions Associated with the Horadam Polynomials , 2018, Iranian Journal of Science and Technology, Transactions A: Science.

[19]  Elizabeth Marquardt,et al.  Truncated expansion of $\zeta_{p^n}$ in the $p$-adic Mal'cev-Neumann field , 2021, 2111.07127.

[20]  G. Murugusundaramoorthy,et al.  Coefficient Bounds for Subclasses of Biunivalent Functions Associated with the Chebyshev Polynomials , 2017 .

[22]  H. Srivastava,et al.  Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma–Minda type , 2017, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas.

[23]  G. MURUGUSUNDARAMOORTHY,et al.  On $lambda$-Pseudo Bi-Starlike Functions with Respect to Symmetric Points Associated to Shell-Like Curves , 2021, Kragujevac Journal of Mathematics.

[24]  See Keong Lee,et al.  Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions , 2012, Appl. Math. Lett..

[25]  The (p, q)-Chebyshev polynomial bounds of a general bi-univalent function class , 2020, Boletín de la Sociedad Matemática Mexicana.

[26]  T. G. Shaba.  On some new subclass of bi-univalent functions associated with the Opoola differential operator , 2020 .

[27]  H. Srivastava,et al.  The Fekete-Szegö functional problems for some subclasses of m-fold symmetric bi-univalent functions , 2016 .

[28]  Ravi P. Agarwal,et al.  Applications of q-Calculus in Operator Theory , 2013 .

[29]  Second Hankel Determinant for Certain Subclasses of Bi-univalent functions , 2020 .

[30]  M. Lewin,et al.  On a coefficient problem for bi-univalent functions , 1967 .

[31]  H. Srivastava,et al.  Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator , 2020, Mathematics.

[32]  T. M. Seoudy,et al.  Coefficient estimates of new classes of q-starlike and q-convex functions of complex order , 2016 .

[33]  A. Akgül.  (P,Q)-Lucas polynomial coefficient inequalities of the bi-univalent function class , 2019, TURKISH JOURNAL OF MATHEMATICS.

[34]  Maslina Darus,et al.  A Subclass of Harmonic Univalent Functions Associated with -Analogue of Dziok-Srivastava Operator , 2013 .

[35]  F. H. Jackson.  XI.—On q-Functions and a certain Difference Operator , 1909, Transactions of the Royal Society of Edinburgh.

[36]  Second Hankel determinant for certain subclasses ofbi-univalent functions , 2017 .

[37]  H. Srivastava,et al.  The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator , 2018, Studia Universitatis Babes-Bolyai Matematica.

[38]  T. G. Shaba,et al.  ON A NEW SUBCLASS OF BI-PSEUDO-STARLIKE FUNCTIONS DEFINED BY FRASIN DIFFERENTIAL OPERATOR , 2020 .

[39]  H. Al-dweby.  Coefficient Estimates for Initial Taylor-Maclaurin Coefficients for a Subclass of Analytic and Bi-univalent Functions Associated with q-Derivative Operator , 2018 .

[40]  W. Tingting,et al.  Some identities involving Fibonacci, Lucas polynomials and their applications , 2012 .

[41]  H. Srivastava,et al.  Coefficient estimates for some general subclasses of analytic and bi-univalent functions , 2017 .