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Abstract
In this paper, we study a new iterative method for finding a common element of the set of solutions of a new general system of variational inequalities for two different relaxed cocoercive mappings and the set of fixed points of a nonexpansive mapping in real 2-uniformly smooth and uniformly convex Banach spaces. We prove the strong convergence of the proposed iterative method without the condition of weakly sequentially continuous duality mapping. Our result improves and extends the corresponding results announced by many others. MSC: 46B10; 46B20; 47H10; 49J40
Highlights
Let X be a real Banach space and X∗ be its dual space
In this paper, motivated and inspired by the idea of Katchang and Kumam [ ] and Yao et al [ ], we introduce a new iterative method for finding a common element of the set of solutions of a new general system of variational inequalities in Banach spaces for two different relaxed cocoercive mappings and the set of fixed points of a nonexpansive mapping in real -uniformly smooth and uniformly convex Banach spaces
We prove the strong convergence of the proposed iterative algorithm without the condition of weakly sequentially continuous duality mapping
Summary
Let X be a real Banach space and X∗ be its dual space. Let C be a subset of X and let T be a self-mapping of C. Which is called the system of general variational inequalities in a real Banach space and the set of solutions of problem In this paper, motivated and inspired by the idea of Katchang and Kumam [ ] and Yao et al [ ], we introduce a new iterative method for finding a common element of the set of solutions of a new general system of variational inequalities in Banach spaces for two different relaxed cocoercive mappings and the set of fixed points of a nonexpansive mapping in real -uniformly smooth and uniformly convex Banach spaces.
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