Data dependence results of a new multistep and S-iterative schemes for contractive-like operators

In this paper, we prove that convergence of a new iteration and S-iteration can be used to approximate to the fixed points of contractive-like operators. We also prove some data dependence results of this new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature.Comment: arXiv admin note: text overlap with arXiv:1211.570

Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process

The purpose of this paper is to introduce the random Picard-Mann hybrid iterative process. We establish the strong convergence theorems and summable almost T-stability of the random Picard-Mann hybrid iterative process and the random Mann-type iterative process generated by a generalized class of random operators in separable Banach spaces. Our results are generalizations and improvements of several well-known deterministic stability results in a stochastic versio

Solution of nonlinear equations using Mann iteration

In this paper, we recall some basic concepts, properties of the spaces and some types of iteration approaches. Also, we give algorithm - fixed point iteration scheme and examples. Finally, we obtain the solution of nonlinear equations of the form using Mann iteration

Common fixed points of two quasicontractive operators in normed spaces by iteration, Int

Abstract. We prove a theorem to approximate common fixed points of two quasi-contractive operators on a normed space through an iteration process with errors and more general than the Ishikawa iteration process.Our result generalizes and improves upon, among others, the corresponding result of Berinde Mathematics Subject Classification: 47H10, 54H2

Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process

Abstract The purpose of this paper is to introduce the random Picard-Mann hybrid iterative process. We establish the strong convergence theorems and summable almost T-stability of the random Picard-Mann hybrid iterative process and the random Mann-type iterative process generated by a generalized class of random operators in separable Banach spaces. Our results are generalizations and improvements of several well-known deterministic stability results in a stochastic version. MSC: 47H09; 47H10; 49M05; 54H25 Keywords: random Picard-Mann hybrid iterative process; random Mann-type iterative process; separable Banach spaces; generalized random contractive type operator; summable almost T-stabilit

On Modified Picard−S−AK Hybrid Iterative Algorithm for Approximating Fixed Point of Banach Contraction Map

The purpose of this work is to introduce a new iteration called the modified Picard-S-AK hybrid iterative scheme for approximating fixed point for Banach contractive maps. We show that our scheme converges to a unique fixed point p at a rate faster than the recent AK iterative scheme for Banach contractive maps. Furthermore, using Java programming language, we give some numerical examples to justify our claim. Stability and data dependence of the proposed scheme are also explored