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We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…
The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…
Suppose that E is a Banach space, {\tau} a topology under which the norm of E becomes {\tau}-lower semicontinuous and S a commuting family of {\tau}-continuous nonexpansive mappings defined on a {\tau}-compact convex subset C of E: It is…
We prove a fixed point theorem for a family of Banach spaces, notably L^1 and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the "derivation problem" studied since the 1960s.
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include $L^1$ and total…
In this paper, we introduced a three-step iterative process with errors for three multivalued mappings satisfying the condition (C) in uniformly convex Banach spaces and establish strong convergence theorems for the proposed process under…
The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…
Very recently, Berinde and P\u{a}curar obtained in [V. Berinde and M. P\u{a}curar, Approximating fixed points of enriched contractions in Banach spaces. Journal of Fixed Point Theory and Applications. \textbf{22}(2) (2020), 1--10.] an…
Let $(X,\|.\|)$ be a Banach space. Let $C$ be a nonempty, bounded, closed, and convex subset of $X$ and $T: C \rightarrow C$ be a $G$-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by…
We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of computable nonexpansive self-maps of a nonempty, computably weakly…
The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
In this paper, by establishing a new characterization of the notion of upper semi-continuity of multi-valued mappings in generalized Banach spaces, we prove some Perov type fixed point theorems for multi-valued mappings with closed graphs.…
In this paper, we consider the Halpern iteration scheme for a finite family of quasinonexpansive mappings and then prove a strong convergence theorem to their common fixed point in a complete geodesic space with curvature bounded above by…
The present research work proposes a new fast fixed-point averaging algorithm on the compact Stiefel manifold based on a mixed retraction/lifting pair. Numerical comparisons between fixed-point algorithms based on the proposed…
In this paper, we consider the CQ projection method and the shrinking projection method given by a finite family of nonexpansive mappings of the unit sphere of a real Hilbert space, and prove strong convergence theorems to common fixed…
This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman-Forchheimer equations, with applications to reverse osmosis. The model…