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Distances between Maximal Monotone Operators
We introduce a series of distances between maximal monotone operators and study their properties. As applications, we consider the existence of...
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Fast Continuous Dynamics Inside the Graph of Maximally Monotone Operators
In a Hilbert framework, we introduce a new class of fast continuous dissipative dynamical systems for approximating zeroes of an arbitrary maximally...
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Operator Inequalities Involving Operator Monotone Functions
In this chapter, we gather improvements of known operator inequalities involving positive linear maps, geometric means, operator monotone functions,...
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Two-step inertial forward–reflected–anchored–backward splitting algorithm for solving monotone inclusion problems
The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of...
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Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of...
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Mirror Frameworks for Relatively Lipschitz and Monotone-Like Variational Inequalities
Nonconvex–nonconcave saddle-point optimization in machine learning has triggered lots of research for studying non-monotone variational inequalities...
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On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems
We present three novel algorithms based on the forward-backward splitting technique for the solution of monotone inclusion problems in real Hilbert...
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Forward-partial inverse-half-forward splitting algorithm for solving monotone inclusions
In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to...
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Abstract Wave Equation with Monotone Operator Dam** in Banach Spaces
This manuscript focuses on the study of the existence of a solution for an abstract Cauchy problem involving a wave equation with a monotone operator...
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Nonlinear operator extensions of Korovkin’s theorems
In this paper we extend Korovkin’s theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function...
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Numerical Methods for Some Classes of Variational Inequalities with Relatively Strongly Monotone Operators
AbstractThe paper deals with a significant extension of the recently proposed class of relatively strongly convex optimization problems in spaces...
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An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward...
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Strong Convergence of the Regularized Operator Extrapolation Algorithm For Variational Inequalities
The authors propose and investigate a new algorithm for solving variational inequalities in Hilbert spaces. The proposed iterative algorithm is...
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Convergence of maximal monotone operators in a Hilbert space
We consider some questions on G -convergence of a sequence of Nemytskii maximal monotone operators defined on the space of square integrable functions...
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Modified inertial viscosity extrapolation method for solving quasi-monotone variational inequality and fixed point problems in real Hilbert spaces
In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed...
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On the proximal map** for multi-valued monotone variational inequality problems
We extend the concept of the proximal map** of a real valued function on a convex set to the one of a multi-valued operator, and study its fixed...
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Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity
In this paper, we study the concept of split monotone variational inclusion problem with multiple output sets. We propose a new relaxed inertial...
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Strong Convergence of Forward–Reflected–Backward Splitting Methods for Solving Monotone Inclusions with Applications to Image Restoration and Optimal Control
In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method of Malitsky and Tam for...
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On the FPV Property, Monotone Operator Structure and the Monotone Polar of Representable Monotone Sets
We study the pointwise partial ordering of representative functions for a monotone operator and in particular we focus on the bigger conjugate...
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Third Order Dynamical Systems for the Sum of Two Generalized Monotone Operators
In this paper, we propose and analyze a third-order dynamical system for finding zeros of the sum of two generalized operators in a Hilbert space
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