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In this paper, we deal with the strong convergence of the iteration scheme given by Akutsah et al., for mean nonexpansive mappings in uniformly convex Banach space endowed with directed graph. Also, we show fastness of Akutsah et al. iteration scheme with some well-known iteration schemes with the help of numerical examples. We, also present an application of fixed point theory in solution of integral equation. [ABSTRACT FROM AUTHOR]

We give a brief account on a basic result (Lemma 3.2) which is a very useful tool in proving various convergence theorems in the framework of the iterative approximation of fixed points of demicontractive mappings in Hilbert spaces. This Lemma relates the class of quasi-nonexpansive mappings, by one hand, and the class of k-demicontractive mappings (quasi k-strict pseudocontractions), on the other hand and essentially states that the class of demicontractive mappings, which strictly includes the class of quasi-nonexpansive mappings, can be embedded in the later by means of an averaged perturbation. From the point of view of the fixed point problem, this means that any convergence result for Krasnoselskij-Mann iterative algorithms in the class of k-demicontractive mappings can be derived from its corresponding counterpart from quasi-nonexpansive mappings. [ABSTRACT FROM AUTHOR]

The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings established by the authors and their collaborators by using this technique; and third, to survey some related developments in the very recent literature which were authored by other researchers. [ABSTRACT FROM AUTHOR]

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified Halpern extragradient-type algorithm for approximating an element in the intersection of the set of common solutions of equilibrium problems and common fixed points of family of nonexpansive mappings in a complete CAT(0) space. We establish strong convergence theorem that improve and generalize recently announced results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a monotone (α, β)-nonexpansive mapping in an ordered Banach space E with the partial order ≤ and prove some existence theorems of fixed points of a monotone (α, β)-nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of Ishikawa type iteration under the control condition ... Finally, we give an numerical example to illustrate the main result in this paper. [ABSTRACT FROM AUTHOR]

new inertial iterative algorithm for approximating solution of split equality fixed point problem (SEFPP) for quasi-ϕ-nonexpansive mappings is introduced and studied in p-uniformly convex and uniformly smooth real Banach spaces, p > 1. A strong convergence theorem is proved without imposing any compactness-type condition on the mappings. Our theorems complement several important recent results that have been proved in 2-uniformly convex and uniformly smooth real Banach spaces. It is well known that these spaces do not include Lp, lp and the Sobolev spaces Wmp(Ω), for 2 < p < ∞. Our theorems, in particular, are applicable in these spaces. Furthermore, application of our theorem to split equality variational inclusion problem is presented. Finally, numerical examples are presented to illustrate the convergence of our algorithms. [ABSTRACT FROM AUTHOR]