Related papers: The fixed point problem for systems of coordinate-…

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…

We prove a new fixed point theorem of Schauder-type which applies to discontinuous operators in non-compact domains. In order to do so, we present a modification of a recent Schauder-type theorem due to Pouso. We apply our result to…

We introduce a new fixed point theorem of Krasnoselskii type for discontinuous operators. As an application we use it to study the existence of positive solutions of a second-order differential problem with separated boundary conditions and…

In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point Algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong, and linear convergence…

In this work, we study fixed point algorithms for finding a zero in the sum of $n\geq 2$ maximally monotone operators by using their resolvents. More precisely, we consider the class of such algorithms where each resolvent is evaluated only…

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…

In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.

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 show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…

In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive…

Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are…

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,…

Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on…

The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…

Monotone systems are dynamical systems whose solutions preserve a partial order in the initial condition for all positive times. It stands to reason that some systems may preserve a partial order only after some initial transient. These…

In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or…

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…

This paper investigates the distributed fixed point finding problem for a global operator over a directed and unbalanced multi-agent network, where the global operator is quasinonexpansive and only partially accessible to each individual…