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The article presents the discussion on making use of Beta negative binomial distribution series normalizing holomorphic and bi-univalent functions involving the Ozaki-close-to-convex functions .

In this paper, we use the (M,N)-Lucas polynomials to establish upper bounds for the second and third coeficients of functions belonging to a new family of of λ-pseudo bi-starlike and λ-pseudo bi-convex functions with respect to symmetrical points defined in the open unit disk D. Also, we discuss the Fekete-Szegfio problem for functions which belong to this family. [ABSTRACT FROM AUTHOR]

In the paper, by using the Horadam polynomials we introduce a new family of analytic and bi-univalent functions which involves a linear combination between Bazilevič functions and λ-pseudo-starlike functions. Then, we obtain upper bounds for the first two Taylor-Maclaurin coefficients |a2| and |a³| of a functions that belongs to this new family. Also, we discuss Fekete-Szegö problem in this new family. Further, we point out several certain special cases of our results. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new subclass of analytic and bi-univalent functions with respect to symmetric conjugate defined in the open unit disk U and obtain an upper bounds for the second Hankel determinant H2(2) of the functions that belong to this class. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate a new family of holomorphic and bi-univalent functions with respect to symmetric conjugate points by using the Horadam polynomials and find upper bounds for the second and third coefficients. Fekete-Szegö problem for functions belonging to this family is solved. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new class of multivalent prestarlike analytic functions with negative coefficients. The authors study some important geometric properties such as coefficients estimates, an integral representation and some subordination properties. Also, we obtain integral mean inequalities for the fractional integral of order λ. [ABSTRACT FROM AUTHOR]

In this present paper, we obtain some applications of first order differential subordination and superordination results involving Hadamard product for multivalent analytic functions with generalized hypergeometric function in the open unit disk. These results are applied to obtain sandwich results. Many of the well-known and new results are shown to follow as special cases of our results. [ABSTRACT FROM AUTHOR]

By making use of the principle of subordination, we introduce a new class for higher-order derivatives of multivalent analytic functions associated with Dziok- Srivastava operator. Also we obtain some results for this class. [ABSTRACT FROM AUTHOR]