In this paper, we establish some convergence results for a monotone nonexpansive mapping in a space. We prove the Δ- and strong convergence of the Mann iteration scheme. Further, we provide a numerical example to illustrate the convergence of our iteration scheme, and also, as an application, we discuss the solution of integral equation. Our results extend some of the relevant results.
In this paper, we propose a three-step iteration process and show that this
process converges faster than a number of existing iteration processes. We
give a numerical example followed by graphs to validate our claim. We prove
strong and weak convergence results for approximating common fixed points
for two nonexpansive mappings. Again we reconfirm our results by examples
and tables. Further, we provide some applications of the our iteration
process.
<abstract><p>Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove $ \Delta $ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.</p></abstract>
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