The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...

We show that if X is a separable Banach space (or more generally a Banach with an infinite-dimensional separable quotient) then there is a continuous mapping f : X → X such that the autonomous differential equation x′ = f(x) has no solution at any point. In order to put our results into context, let us start by formulating the classical theorem of Peano. Theorem 1. (Peano) Let X = R, f : R×X → ...

In this paper, we first prove weak and strong convergence theorems for Ishikawa and Halpern iterations of 2-generalized hybrid mappings in uniformly convex Banach spaces and we apply our method to provide an affirmative answer to an open problem raised by Hojo, Takahashi and Termwuttipong [Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces, Nonlinear Analysis, 75 (2...

We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of countable family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection techniqu...

Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong c...

In this paper, we first introduce a family S = {Sn : C → C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence {xn} defined recursively by the algorithm xn+1 = Snxn, n ≥ 1, starting from an initial guess x1 ∈ C...

The primary objective of the paper is to present Banach contraction theorem in soft fuzzy metric spaces while taking into consideration a restriction on between points absolute set. A new altering distance function, namely Ψ-contraction introduced spaces, and some fixed point results are proven by considering mappings that comprise with continuity t-norm. In addition that, illustrations supplie...