Fixed point solutions for variational inequalities in image restoration over q-uniformly smooth Banach spaces
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Author list: Sunthrayuth P., Kumam P.
Publisher: SpringerOpen
Publication year: 2014
Journal: Journal of Inequalities and Applications (1025-5834)
Volume number: 2014
Issue number: 1
ISSN: 1025-5834
eISSN: 1029-242X
Languages: English-Great Britain (EN-GB)
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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 [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.] spaces with [InlineEquation not available: see fulltext.]. 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. MSC:47H09, 47H10, 47H17, 47J25, 49J40. ฉ 2014, Sunthrayuth and Kumam; licensee Springer.
Keywords
strongly accretive operator
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