Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme.

A New Modified Fixed-Point Iteration Process

In this paper, we present a new modified iteration process in the setting of uniformly convex Banach space. The newly obtained iteration process can be used to approximate a common fixed point of three nonexpansive mappings. We have obtained strong and weak convergence results for three nonexpansive mappings. Additionally, we have provided an example to support the theoretical proof. In the process, several relevant results are improved and generalized.

On the JK Iterative Process in Banach Spaces

In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α -nonexpansive mappings. Secondly, by constructing an example of generalized α -nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature.

Some Convergence Results for a Class of Generalized Nonexpansive Mappings in Banach Spaces

This paper investigates fixed points of Reich-Suzuki-type nonexpansive mappings in the context of uniformly convex Banach spaces through an M ∗ iterative method. Under some appropriate situations, some strong and weak convergence theorems are established. To support our results, a new example of Reich-Suzuki-type nonexpansive mappings is presented which exceeds the class of Suzuki-type nonexpansive mappings. The presented results extend some recently announced results of current literature.

Strong and weak convergence theorems for general mixed equilibrium problems and general variational inequality problems and fixed point problems for two nonexpansive semigroups in Hilbert spaces

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of the general mixed equilibrium problem and the set of solutions of a general variational inequality for two cocoercive mappings and the set of common fixed points of two nonexpansive semigroups in Hilbert space. We obtain both strong and weak convergence theorems for the sequences generated by these iterative processes in Hilbert spaces. Our results improve and extend the results announced by many others.

On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces

In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature.

Convergence theorems for mixed type iterative process of single-valued and multi-valued nonexpansive mappings and applications

In this paper, we introduce a new mixed type iterative process, which approximates the common fixed points of single-valued nonexpansive mappings and two multi-valued nonexpansive mappings in a uniformly convex Banach space. We establish strong and weak convergence theorems for the new iterative process in Banach space and give their corresponding applications.