scholarly journals Accelerated modified inertial Mann and viscosity algorithms to find a fixed point of $ \alpha - $inverse strongly monotone operators

2021 ◽  
Vol 6 (8) ◽  
pp. 9000-9019
Author(s):  
Hasanen A. Hammad ◽  
◽  
Habib ur Rehman ◽  
Manuel De la Sen ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Monotone Operators ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Operators

scholarly journals Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Caiping Yang ◽  
Songnian He
Keyword(s):  
Variational Inequality ◽  
Unique Solution ◽  
Real Hilbert Space ◽  
Iterative Algorithms ◽  
Monotone Operators ◽  
Strongly Monotone ◽  
Lipschitz Constants ◽  
Strongly Monotone Operators ◽  
Original Domain ◽  
Self Adaptive

Consider the variational inequalityVI(C,F)of finding a pointx*∈Csatisfying the property〈Fx*,x-x*〉≥0for allx∈C, whereCis a level set of a convex function defined on a real Hilbert spaceHandF:H→His a boundedly Lipschitzian (i.e., Lipschitzian on bounded subsets ofH) and strongly monotone operator. He and Xu proved that this variational inequality has a unique solution and devised iterative algorithms to approximate this solution (see He and Xu, 2009). In this paper, relaxed and self-adaptive iterative algorithms are proposed for computing this unique solution. Since our algorithms avoid calculating the projectionPC(calculatingPCby computing a sequence of projections onto half-spaces containing the original domainC) directly and select the stepsizes through a self-adaptive way (having no need to know any information of bounded Lipschitz constants ofF(i.e., Lipschitz constants on some bounded subsets ofH)), the implementations of our algorithms are very easy. The algorithms in this paper improve and extend the corresponding results of He and Xu.

An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

2018 ◽  
Vol 9 (3) ◽  
pp. 167-184 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Ferdinard Udochukwu Ogbuisi ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Monotone Operators ◽  
Convergence Result ◽  
Reflexive Banach Spaces ◽  
Strongly Monotone Operators ◽  
System Of Equilibrium Problems

Abstract In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

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