1. Fixed point solutions for variational inequalities in image restoration over q-uniformly smooth Banach spaces.
- Author
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Sunthrayuth, Pongsakorn and Kumam, Poom
- Subjects
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VARIATIONAL inequalities (Mathematics) , *BANACH spaces , *FIXED point theory , *IMAGE reconstruction , *STOCHASTIC convergence , *LINEAR operators , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
In this paper, we introduce new implicit and explicit iterative methods for finding a common fixed point set of an infinite family of strict pseudo-contractions by the sunny nonexpansive retractions in a real q-uniformly and uniformly convex Banach space which admits a weakly sequentially continuous generalized duality mapping. Then we prove the strong convergence under mild conditions of the purposed iterative scheme to a common fixed point of an infinite family of strict pseudo-contractions which is a solution of some variational inequalities. Furthermore, we apply our results to study some strong convergence theorems in Lp and ℓp spaces with 1 < p <∞. Our results mainly improve and extend the results announced by Ceng et al. (Comput. Math. Appl. 61:2447-2455, 2011) and many authors from Hilbert spaces to Banach spaces. Finally, we give some numerical examples for support our main theorem in the end of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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