Fixed point solutions for variational inequalities in image restoration over q-uniformly smooth Banach spaces
Pongsakorn Sunthrayuth, Poom Kumam · Journal of Inequalities and Applications · 2014
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 L p and ℓ p 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.