In this paper, we determine the sharp upper bounds of Hankel determinants for logarithmic and inverse functions of bounded turning functions associated with the hyperbolic tangent function.

The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Gauss hypergeometric polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Gauss hypergeometric polynomials, \[ $\;_2F_1(-n, a; -n+b;z),$ \] where $n$ is a nonnegative integer. Owing to the connection between the classical Jacobi polynomials and the Gauss hypergeometric polynomials, we prove a special case of a conjecture made by Martínez-Finkelshtein, Martínez-González and Orive. Numerical evidence and graphical illustrations of the clustering of the zeros on certain curves are generated by Mathematica (Version 4.0).

In the present paper, we introduce and investigate some new subclasses of multivalent analytic functions involving the Dziok–Srivastava operator. Such results as inclusion relationships, integral representations, convolution properties and integral-preserving properties for these function classes are proved. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

The main objective of the present paper is to define a subclass $Q_{q}(\lambda,\mu,A,B)$ of analytic functions by using subordination along with the newly defined $q$-analogue of Choi-Saigo-Srivastava operator. Such results as coefficient estimates, integral representation, linear combination, weighted and arithmetic means, and radius of starlikeness for this class are derived.**********************************************************************************************************************************

The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Clausenian hypergeometric $\;_3F_2$ functions and polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Clausenian hypergeometric polynomials: \[ $\;_3F_2(-n, \tau n+a, b;\tau n+c, -n+d;z),$ \] where $n$ is a nonnegative integer. Some families of the hypergeometric $_3F_2$ functions, which are connected (by means of a hypergeometric reduction formula) with the Gauss hypergeometric polynomials of the form \[ $\;_2F_1(-n,kn+l+1;kn+l+2;z),$ \] are also investigated. Numerical evidence and graphical illustrations of the clustering of zeros on certain curves are generated by Mathematica (Version 4.0).