Related papers: On Fej\'er monotone sequences and nonexpansive map…
We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.
We prove that the iterates produced by, either the scalar step size variant, or the coordinatewise variant of AdaGrad algorithm, are convergent sequences when applied to convex objective functions with Lipschitz gradient. The key insight is…
In this paper we introduce FG- coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG- coupled fixed…
In this paper, we introduce a new category of mappings within metric spaces, specifically focusing on three-point analogs of the well-established Chatterjea type mappings. We demonstrate that Chatterjea type mappings and their three-point…
In this paper we establish the existence of related fixed points theorems for two pairs of mappings with different contraction conditions in two fuzzy metric spaces.
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
In this paper, we consider the class of generalized {\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V. V. Chistyakov, Metric modulars and their application, Dokl.…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
Dini's Theorem guarantees that a monotone sequence of continuous functions converges pointwise on a compact interval to a continuous limit that converges uniformly. In this paper, we establish new theorems generalizing Dini's result by…
We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…
Diversities have been recently introduced as a generalization of metrics for which a rich tight span theory could be stated. In this work we take up a number of questions about hyperconvexity, diversities and fixed points of nonexpansive…
We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…
We consider the general second order difference equation $x_{n+1}=F(x_n,x_{n-1})$ in which $F$ is continuous and of mixed monotonicity in its arguments. In equations with negative terms, a persistent set can be a proper subset of the…
In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions.…
Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0,1], with…
In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone…
In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic…