The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences {cn} and {dn} of positive real numbers. By specializing {cn} and {dn}, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined. The theorems presented, in many cases, confirm or ge...

in this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk u.such results as coecientinequalities. the results presented here would provide extensions of those givenin earlier works.

Recently the present authors established refined versions of Bohr's inequality in case bounded analytic functions. In this article, we state and prove a generalization these results. Here, consider image origin boundary unit disk under function question let distance between both play central role our theorems. Thereby extend Bohr for class quasi-subordinations which contains classes majorizatio...

This is an introductory survey on applications of the Julia variation to problems in geometric function theory. A short exposition is given which develops a method for treating extremal problems over classes F of analytic functions on the unit disk D for which appropriate subsets Fn can be constructed so that (i) F = ⋃ n Fn and (ii) for each f ∈ Fn a geometric constraint will hold that ∂f(D) wi...

which are analytic in the open unit disk U {z ∈ C : |z| < 1}. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z if there exists an analytic function w in U with w 0 0 and |w z | < 1 for z ∈ U such that f z g w z . We denote by S∗, K, and C the subclasses of A consisting of all analytic functions which are, respectively, starlike, convex, and close-to-co...

In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto whole complex plane. We also establish connection between boundary functions harmonic and biharmonic mappings. Finally, show how close-to-convex can be constructed from convex mapping.