Functional equations in real-analytic functions

The Fekete-Szego Coefficient Functional for Transforms of Analytic Functions

Analytic Solutions for Iterative Functional Differential Equations

Because of its technical difficulties the existence of analytic solutions to the iterative differential equation x′(z) = x(az + bx(z) + cx′(z)) is a source of open problems. In this article we obtain analytic solutions, using Schauder’s fixed point theorem. Also we present a unique solution which is a nonconstant polynomial in the complex field.

A lethargy result for real analytic functions

We prove that, if (C[a, b], {An}) is an approximation scheme and (An) satisfies de La Vallée-Poussin Theorem, there are instances of continuous functions on [a, b], real analytic on (a, b], which are “poorly approximable” by the elements of {An}. This illustrates the thesis that the smoothness conditions guaranteeing that a function is “well approximable” must be “global”. The failure of smooth...

Some properties of analytic functions related with bounded positive real part

In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.

Functional Equations and Distribution Functions

We consider the functional equation f(t) = 1 b b?1 X =0 f t ? a for all t 2 IR; (F) where 0 < a < 1, b 2 IN n f1g and ?1 = 0 1 : : : b?1 = 1 are given parameters, f : IR ! IR is the unknown. We show that there is a unique bounded function f which solves (F) and satisses f(t) = 0 for t < ?1=(1 ? a), f(t) = 1 for t > 1=(1 ? a). This solution can be interpreted as the distribution function of a ce...