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The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…

Optimization and Control · Mathematics 2021-04-19 Barbara Pascal , Nelly Pustelnik , Patrice Abry

Suppose that $Q$ is a family of seminorms on a locally convex space $E$ which determines the topology of $E$. In this paper, first we define the notation of the $q$-duality mappings in locally convex spaces. Then we introduce an implicit…

Functional Analysis · Mathematics 2021-04-15 Ebrahim Soori , M. R. Omidi , A. P. Farajzadeh , Yuanheng Wang

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…

Optimization and Control · Mathematics 2021-09-21 Lam M. Nguyen , Quoc Tran-Dinh , Dzung T. Phan , Phuong Ha Nguyen , Marten van Dijk

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…

Functional Analysis · Mathematics 2020-02-18 Tatsuki Ezawa

We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.

General Topology · Mathematics 2016-11-25 Hassen Aydi

We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…

Optimization and Control · Mathematics 2025-12-16 Felipe Atenas , Farhana Ahmed Simi , Matthew K Tam

The Halpern algorithm is a powerful fixed point approximation method for finding the closest point in the fixed point set of a nonexpansive mapping to the initial point. However, in practice, it is not necessarily true that this algorithm…

Optimization and Control · Mathematics 2026-04-24 Hideaki Iiduka

A generalized version of both rectangular metric spaces and rectangular quasi-metric spaces is known as rectangular quasi b-metric spaces (RQB-MS). In the current work, we define generalized $( \theta,\phi) $-contraction mappings and study…

Metric Geometry · Mathematics 2024-07-12 Mohamed Rossafi , Abdelkarim Kari

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

Optimization and Control · Mathematics 2017-09-19 Nguyen Hieu Thao

Assume that $X$ is a Banach space of measurable functions for which Koml\'os' Theorem holds. We associate to any closed convex bounded subset $C$ of $X$ a coefficient $t(C)$ which attains its minimum value when $C$ is closed for the…

Functional Analysis · Mathematics 2017-09-12 T. Domínguez Benavides , M. A , Japón

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…

Metric Geometry · Mathematics 2016-10-05 Bozena Piatek , Rafa Espinola

Weintroduce a new class of mappings called cyclic p-$\phi$-contraction mappings and investigate the existence and uniqueness of fixed point for such mappings defined on metric spaces, uniformly convex Banach spaces, or reflex ive Banach…

Functional Analysis · Mathematics 2026-02-19 Seyyed Mohammad Sadegh Nabavi Sales

In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…

Functional Analysis · Mathematics 2010-07-07 Eric U. Ofoedu

We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly…

Optimization and Control · Mathematics 2021-11-30 Sorin-Mihai Grad , Felipe Lara

The main purpose of this paper is to extend some fixed point results for single valued $b$-enriched nonexpansive mappings to the case of multivalued mappings. To this end, we introduce *-$b$-enriched nonexpansive mappings, as a…

Functional Analysis · Mathematics 2025-04-01 Ioan Trifoi

In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…

Optimization and Control · Mathematics 2025-05-06 Radu Ioan Bot , Rossen Nenov , Min Tao

Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…

Optimization and Control · Mathematics 2022-03-29 Hui Ouyang

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…

Optimization and Control · Mathematics 2025-06-10 Minh N. Dao , Tan Nhat Pham , Phan Thanh Tung

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

Optimization and Control · Mathematics 2022-02-22 Francisco J. Aragón-Artacho , Radu I. Boţ , David Torregrosa-Belén

We use $KKM$ theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and $A:M\rightarrow M$ be a non-expansive mapping, then exists a fixed point of A…

Functional Analysis · Mathematics 2012-08-07 Chunyan Yang