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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.

The objective of this article is to study a three-step iteration process in the framework of Banach spaces and to obtain convergence results for Suzuki generalized nonexpansive mappings. We also provide numerical examples that support our main results and illustrate the convergence behavior of the proposed process. Further, we present a data-dependence result that is also supported by a nontrivial numerical example. Finally, we discuss the solution of a nonlinear fractional differential equation by utilizing our results.

<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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<abstract><p>In this article, we present a new modified proximal point algorithm in the framework of CAT(1) spaces which is utilized for solving common fixed point problem and minimization problems. Also, we prove convergence results of the obtained process under some mild conditions. Our results extend and improve several corresponding results of the existing literature.</p></abstract>