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We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone of a partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and the dominated…

Functional Analysis · Mathematics 2023-05-31 Marcel de Jeu , Xingni Jiang

We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of…

Optimization and Control · Mathematics 2023-06-22 Gerd Wachsmuth

Let $X, Y$ be infinite dimensional, Banach spaces. Let $\mathcal{L}(X, Y)$ be the space of bounded operators . Motivated by the fact that smoothness of norm in the higher duals of even order of a Banach space can lead to Frechet…

Functional Analysis · Mathematics 2022-12-13 Taduri Srinivasa Siva Rama Krishna Rao

Suppose $\mathcal{Z}$ is the space of all tuples of operators on a finite-dimensional Banach space endowed with the joint numerical radius norm. We obtain the structure of the extreme points of the dual unit ball of $\mathcal{Z}.$ Using…

Functional Analysis · Mathematics 2025-07-08 Arpita Mal

In this paper, we study Frechet derivatives and Mordukhovich derivatives (or coderivatives) of single-valued mappings in Euclidean spaces. At first, we prove the guideline for calculating the Frechet derivatives of single-valued mappings by…

Functional Analysis · Mathematics 2025-08-20 Jinlu Li

In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…

Optimization and Control · Mathematics 2010-09-09 Boris Mordukhovich , Nguyen Mau Nam

This is the second part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general…

Dynamical Systems · Mathematics 2014-11-06 Janusz Mierczyński , Wenxian Shen

In this paper, the split common null point problem in two Banach spaces is considered. Then, using the generalized resolvents of maximal monotone operators and the generalized projections and an infinite family of nonexpansive mappings, a…

Functional Analysis · Mathematics 2021-03-29 Bijan Orouji , Ebrahim Soori

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…

Combinatorics · Mathematics 2015-01-14 Felix Pogorzelski

The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of…

Functional Analysis · Mathematics 2017-09-14 Fumio Hiai , Jimmie Lawson , Yongdo Lim

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman…

Functional Analysis · Mathematics 2023-04-21 Bijan Orouji , Ebrahim Soori , Donal O'Regan , Ravi P. Agarwal

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…

Probability · Mathematics 2015-07-13 Monica Patriche

In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The…

Functional Analysis · Mathematics 2011-02-09 Ali Abkar , Mohammad Eslamian

In this paper, we investigate a new notion of accretive mappings called generalized $\alpha\beta$-$H((.,.),(.,.))$-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings associated with generalized…

Functional Analysis · Mathematics 2015-10-07 Sanjeev Gupta , Shamshad Husain , Vishnu Narayan Mishra

In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…

Functional Analysis · Mathematics 2020-03-26 M. Alikhani

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.…

Functional Analysis · Mathematics 2024-07-22 Khaled Ben Amara , Aref Jeribi , Najib Kaddachi , Zahra Laouar

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…

Machine Learning · Statistics 2014-01-03 R. A. DeVore , V. N. Temlyakov

We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized…

Analysis of PDEs · Mathematics 2025-03-21 Roland Becker , Malte Braack

This is the first of a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. It focuses on the development of general theory. First, the…

Dynamical Systems · Mathematics 2014-11-06 Janusz Mierczyński , Wenxian Shen

The paper gives some results on best proximity and fixed point for a class of generalized hybrid cyclic self-mappings in Banach spaces.

Functional Analysis · Mathematics 2012-12-27 M. De la Sen