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Solutions of some functional equations in a class of generalized Hölder functions

Lupa M.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 4

105--116

The existence and uniqueness of solutions a nonlinear iterative equation in the class of r-times differentiable functions with the r-derivative satisfying a generalized Hölder condition is considered.

Iterative equations in p-normes spaces

Żołdak M.

Demonstratio Mathematica

2006

Vol. 39, nr 3

571-578

Let X be a real p-normed, complete space and V be a nonempty closed subset of X. We consider the functional equation.

Analytic solutions of a polynomial-like iterative functional equation

Si J., Wang X.

Demonstratio Mathematica

1999

Vol. 32, nr 1

95-103

This paper is concerned with a polynomial-like iterative functional equation lambda1f(z) + lambda2f(2)(z) + .. . . + lambdamf[m](z) = F(z), where f(z) is an unknown function, F(z) is a given function, f[i]l denotes the i-th iterate of f, and lambda1, lambda2, . . .,lambdam are complex constants. By constructing a convergent power series solution phi(z) of an auxiliary equation of the form lambda1alpha(alphaz)+lambda2phi(alpha2z)+.....+lambdamphi(alphamz)=F(phi(z)), analytic solutions of the form phi(alphaphi-1(z)) for the original iterative functional equation are obtained.