Related papers: On Fej\'er monotone sequences and nonexpansive map…
Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate…
We investigate necessary and sufficient conditions for a nonexpansive map $f$ on a Banach space $X$ to have surjective displacement, that is, for $f - \mathrm{id}$ to map onto $X$. In particular, we give a computable necessary and…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
We establish a simple and powerful lemma that provides a criterion for sequences in metric spaces to be Cauchy. Using the lemma, it is then easily verified that the Picard iterates $\{T^nx\}$, where $T$ is a contraction or asymptotic…
This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which…
We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…
In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…
This study presents novel methods for computing fixed points of positive concave mappings and for characterizing the existence of fixed points. These methods are particularly important in planning and optimization tasks in wireless…
In this paper we prove FG-coupled fixed point theorems for different contractive mappings and generalized quasi- contractive mappings in partially ordered complete metric spaces. We prove the existence of FG-coupled fixed points of…
In this paper we give some coupled fixed point results for mappings satisfying different contractive conditions on complete partial metric spaces.
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…
The aim of this paper is to introduce and to investigate the basic properties of $q$-convex, $q$-affine and $q$-concave sequences and to establish their surprising connection to Chebyshev polynomials of the first and of the second kind. One…
We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
Fixed points for uniformly local asymptotic nonexpansive maps are discussed in this article. An approximate fixed point sequence for such a map over a uniformly convex Banach space is derived. At the end, we study the unique fixed point for…
In this paper, we introduce a new contraction condition that combines the framework of Singh's extension with the classical Chatterjea contraction. This generalized form, called the Singh-Chatterjea contraction, is defined on the p-th…