Results 41 to 50 of about 31,881 (213)

Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving (A,η)-Maximal Relaxed Monotone Operators

Journal of Applied Mathematics, 2014
We introduce and study a class of new general systems of set-valued variational inclusions involving (A,η)-maximal relaxed monotone operators in Hilbert spaces.
Ting-jian Xiong, Heng-you Lan
doaj   +1 more source

Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators

Journal of Inequalities and Applications, 2017
In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods.
Tadchai Yuying, Somyot Plubtieng
doaj   +1 more source

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

, 2010
In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions.
A. Moudafi, A. Moudafi, C. Zăalinescu, C. Zălinescu, H. Attouch, H. Attouch, J.-E. Martínez-Legaz, J.M. Borwein, M. Marques Alves, R.I. Boţ, R.I. Boţ, R.I. Boţ, R.T. Rockafellar, Radu Ioan Boţ, S. Bartz, S. Simons, Sorin-Mihai Grad   +16 more
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An Answer to S. Simons’ Question on the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Operator and a Normal Cone Operator [PDF]

Set-Valued and Variational Analysis, 2009
The question whether or not the sum of two maximal monotone operators is maximal monotone under Rockafellar's constraint qualification - that is, whether or not "the sum theorem" is true - is the most famous open problem in Monotone Operator Theory. In his 2008 monograph "From Hahn-Banach to Monotonicity", Stephen Simons asked whether or not the sum ...
Heinz H. Bauschke, Liangjin Yao, Xianfu Wang   +2 more
openaire   +3 more sources

Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems

, 2014
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another ...
Andrea Porras-Alfaro (3275619), Emily C. Farrer (2926542), Katharine N. Suding (331341), Robert L. Sinsabaugh (2905805), Sarah L. Dean (3275622)   +4 more
core   +3 more sources

Convergence theorems for split feasibility problems on a finite sum of monotone operators and a family of nonexpansive mappings

Journal of Inequalities and Applications, 2018
In this paper, we present two iterative algorithms for approximating a solution of the split feasibility problem on zeros of a sum of monotone operators and fixed points of a finite family of nonexpansive mappings.
Narin Petrot, Montira Suwannaprapa, Vahid Dadashi   +2 more
doaj   +1 more source

Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications

Abstract and Applied Analysis, 2012
The purpose of this paper is to present the notion of weak relatively nonexpansive multi-valued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces.
Jingling Zhang, Yongfu Su, Qingqing Cheng   +2 more
doaj   +1 more source

Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces

, 1998
We use the relative modular operator to define a generalized relative entropy for any convex operator function g on the positive real line satisfying g(1) = 0.
Lesniewski, Andrew, Ruskai, Mary Beth
core   +1 more source

Convergence analysis of a variable metric forward–backward splitting algorithm with applications

Journal of Inequalities and Applications, 2019
The forward–backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and an inverse strongly monotone operator.
Fuying Cui, Yuchao Tang, Chuanxi Zhu
doaj   +1 more source

Perturbations of maximal monotone random operators

Linear Algebra and its Applications, 1986
AbstractLet X be a Banach space, X∗ its dual, and Ω a measurable space. We study the solvability of nonlinear random equations involving operators of the form L + T, where L is a maximal monotone random operator from Ω × X into X∗ and T : Ω × X → X∗ a random operator of monotone type.
Nicolaos Stavrakakis, Dimitrios Kravvaritis   +1 more
openaire   +2 more sources