in this article we study steensen method to solve nonlinear matrix equation x+a^t x^(-1) a=q, when a is a normal matrix. we establish some conditions that generate a sequence of positive de nite matrices which converges to solution of this equation.

in this paper we investigate the generalized hyers-ulamstability of the following cauchy-jensen type functional equation$$qbig(frac{x+y}{2}+zbig)+qbig(frac{x+z}{2}+ybig)+qbig(frac{z+y}{2}+xbig)=2[q(x)+q(y)+q(z)]$$ in non-archimedean spaces

let $c$ be a nonempty closed convex subset of a real hilbert space $h$. let ${s_n}$ and ${t_n}$ be sequences of nonexpansive self-mappings of $c$, where one of them is a strongly nonexpansive sequence. k. aoyama and y. kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1-beta_n)s_n(alpha_nu+(1-alpha_n)t_nx_n)$ for finding the common fixed point of ${s_n}$ and ${t_n}$, where $uin c$ is ...

We discuss the problem of finding approximate solutions of the equation 0 ) (  x f (1) In some cases it is possible to find the exact roots of the equation (1) for example when ) (x f is a quadratic on cubic polynomial otherwise, in general, is interested in finding approximate solutions using some numerical methods. Here, we will discuss a method called fixed point iteration method and a part...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...