Some Special Families of Holomorphic and Sălăgean Type Bi-univalent Functions Associated with \((m,n)\)-Lucas Polynomials

S. R. Swamy, Abbas Kareem Wanas, Y. Sailaja


The aim of the present paper is to introduce some special families of holomorphic and Sălăgean type bi-univalent functions associated with \((m,n)\)-Lucas polynomials in the open unit disc \(\mathfrak{D}\). We investigate the upper bounds on initial coefficients for functions in these newly introduced special families and also discuss the Fekete-Szegö problem.\ Some interesting consequences of the results established here are indicated.


Holomorphic function; Bi-univalent function; Fekete-Szegö inequality; Lucas polynomial; Sălăgean operator

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