In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

This note contains a short review of the notion of linearization of regular matrix polynomials. The objective is clarification of this notion when the polynomial has an “eigenvalue at infinity”. The theory is extended to admit reduction by locally unimodular analytic matrix functions.

The present paper is concerned with the fast growth of analytic functions in the sets of the form {z C : φK(z) < R} (where φK(z) is the Siciak extremal function of a compact set K) by means of the Lagrange polynomial approximation and interpolation on K having rapidly increasing maximum modulus. To study the precise rates of growth of such functions the concept of index has been used.

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...

By utilizing the concept of q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass A, where class A contains normalized analytic functions in open unit disk E is invariant or symmetric under rotation. First, using Faber polynomial expansion (FPE) technique, determine lth coefficient bound for contained within this class. We provide further explanation first ...

It is shown that, an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively. 1

For analytic functions f (z) = z p +a p+1 z p+1 +··· in the open unit disk U and a polynomial Q(z) of degree n > 0, the function F(z) = f (z)[Q(z)] β/n is introduced. The object of the present paper is to determine the radius of p-valently strongly starlikeness of order γ for F(z).

If P(z) be a polynomial of degree n with decreasing coefficients, then all its zeros lie in |z| ≤ 1. In this paper we find new classical results concerning Enestrom-Kakeya theorem and related analytic functions. Besides several consequences, our results improve the bounds by relaxing and weakening the hypothesis in some cases.

We prove a conjecture of [3] giving a closed form formula for the norm of the Jack polynomials in superspace with respect to a certain scalar product. The proof is mainly combinatorial and relies on the explicit expression in terms of admissible tableaux of the non-symmetric Jack polynomials. In the final step of the proof appears an identity on weighted sums of partitions that we demonstrate u...

let a(p) denote the class of functions which are analytic in the open unit disk u. by making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.