Results 21 to 30 of about 1,184,775 (281)

Bregman Distance and Strong Convergence of Proximal-Type Algorithms

Abstract and Applied Analysis, 2013
The purpose of this paper is to discuss some fundamental properties of Bregman distance, generalized projection operators, firmly nonexpansive mappings, and resolvent operators of set-valued monotone operators corresponding to a functional Φ(∥·∥).
Li-Wei Kuo, D. R. Sahu
doaj   +1 more source

The Resolvent Average of Monotone Operators: Dominant and Recessive Properties [PDF]

SIAM Journal on Optimization, 2015
Within convex analysis, a rich theory with various applications has been evolving since the proximal average of convex functions was first introduced over a decade ago.
Sedi Bartz, Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang   +3 more
semanticscholar   +1 more source

Random Fixed Point Theorems of Random Comparable Operators and an Application

Discrete Dynamics in Nature and Society, 2015
We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces.
Jiandong Yin, Zhongdong Liu
doaj   +1 more source

Approximation solvability for a system of implicit nonlinear variational inclusions with Η-monotone operators

Demonstratio Mathematica, 2018
In this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces.
Kim Jong Kyu, Bhat Muhammad Iqbal
doaj   +1 more source

Iterative Methods for the Sum of Two Monotone Operators

Journal of Applied Mathematics, 2012
We introduce an iterative for finding the zeros point of the sum of two monotone operators. We prove that the suggested method converges strongly to the zeros point of the sum of two monotone operators.
Yeong-Cheng Liou
doaj   +1 more source

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

SIAM Review, 2020
This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is coupled with a static or time-varying set-valued operator in the feed...
B. Brogliato, A. Tanwani
semanticscholar   +1 more source

Monotone versus non‐monotone projective operators

Bulletin of the London Mathematical Society
AbstractFor a class of operators , let denote the closure ordinal of ‐inductive definitions. We give upper bounds on the values of and under the assumption that all projective sets of reals are determined, significantly improving the known results.
J. P. Aguilera, P. D. Welch
openaire   +3 more sources

Strong Convergence Theorems for Maximal Monotone Operators with Nonspreading Mappings in a Hilbert Space

Abstract and Applied Analysis, 2012
We prove the strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mapping T and the solution sets of zero of a maximal monotone mapping and an α-inverse strongly monotone mapping in a Hilbert space. Manaka
Hongjie Liu, Junqing Wang, Qiansheng Feng   +2 more
doaj   +1 more source

Bishop-Phelps-Bollobás property for positive operators when the domain is L∞

Bulletin of Mathematical Sciences, 2021
We prove that the class of positive operators from L∞(μ) to Y has the Bishop-Phelps-Bollobás property for any positive measure μ, whenever Y is a uniformly monotone Banach lattice with a weak unit.
María D. Acosta, Maryam Soleimani-Mourchehkhorti   +1 more
doaj   +1 more source

Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure

Advances in Nonlinear Analysis, 2020
In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators.
Boţ Radu Ioan, Grad Sorin-Mihai, Meier Dennis, Staudigl Mathias   +3 more
doaj   +1 more source