iterative algorithm

In this paper, we introduce a new iterative algorithm for finding a common solution for variational inclusion problem and fixed point problem in real Hilbert spaces. This method can be implemented more easily without the prior knowledge of the Lipschitz constant of component operators. The algorithm uses variable step-sizes which are updated at each iteration by a simple computation. In additional, weak and strong convergence results of the proposed algorithm are obtained under some mild conditions. Then, we establish the linear rate of convergence for the proposed algorithm. Finally, an example is given to illustrate the convergence of the algorithm.

In this paper, we prove that a faster iterative algorithm can be used to reach the solution of the Volterra functional integral equation of the second kind. Also, we show that a data dependence result can be obtained for this integral equation and to support this result we give an example.

In this paper, we introduce and study a system of generalized quasi-variational inequalities involving nonlinear, nonconvex and nondifferentiable terms in uniformly smooth Banach space. By means of the retraction mapping technique, we prove the existence of solutions for this system of quasi-variational inequalities. Further, we suggest an iterative algorithm for finding the approximate solution of this system and discuss the convergence criteria of the sequences generated by the iterative algorithm under some suitable conditions.

In this manuscript, we introduce and study the existence of a solution of a system of generalized nonlinear variational-like inclusion problems in 2-uniformly smooth Banach spaces by using $H(.,.)$-$eta$-proximal mapping. The method used in this paper can be considered as an extension of methods for studying the existence of solutions of various classes of variational inclusions considered and studied by many authors in 2-uniformly smooth Banach spaces. Some important results, theorems and the existence of solution of the proposed system of generalized nonlinear variational-like inclusion problems have been derived.

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and generalized Yosida approximation operator. We also furnish an illustrative example to demonstrate our results. Furthermore, we suggest an iterative algorithm to solve a Yosida inclusion problem under some mild conditions in q-uniformly smooth Banach space and discuss the convergence and uniqueness of the solution.

In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained coupled linear matrix equations. Numerical experiments are presented to demonstrate the applicably and efficiency of our method.

Consider the following consistent Sylvester tensor equation
X×1A×2B×3C=D,
where the matrices A,B,C and the tensor D are given and X is the unknown tensor. The current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and its modified version for solving the mentioned Sylvester tensor equation without setting the restriction of the existence of a unique solution. Numerical experiments are reported which confirm the validity of the presented results.

In this paper, we introduce an iterative algorithm free from second derivative for solving algebraic nonlinear equations. The analysis of convergence shows that this iterative algorithm has seventh order convergence. Per iteration of the new algorithm requires three evaluations of the function and two evaluation of its rst derivative. Therefore this algorithm has the eciency index which equals to 1.477. The results obtained using the algorithm presented here show that the iterative algorithm is very eective and convenient for the algebraic nonlinear equations.

Some algorithms for nding common xed point of a family of mappings is constructed. Indeed, let C be a nonempty closed convex subset of a uniformly convex Banach space X whose norm is Gateaux di erentiable and let {Tn} be a family of self-mappings on C such that the set of all common fixed points of {Tn} is nonempty. We construct a sequence {xn} generated by the hybrid method and also we give the conditions of {Tn} under which {xn} converges strongly to a common xed point of {Tn}.