Abstract
In this paper, we introduce new iterative algorithms for finding a common element of the set of solutions of a general system of nonlinear variational inequalities with perturbed mappings and the set of common fixed points of a one-parameter nonexpansive semigroup in Banach spaces. Furthermore, we prove the strong convergence theorems of the sequence generated by these iterative algorithms under some suitable conditions. The results obtained in this paper extend the recent ones announced by many others.Mathematics Subject Classification (2010): 47H09, 47J05, 47J25, 49J40, 65J15
Highlights
Variational inequality theory has been studied widely in several branches of pure and applied sciences
Where C is the fixed point set of a nonexpansive mapping T on H and u is a given point in H
We show that our iterative algorithm converges strongly to a common element of the two aforementioned sets under some suitable conditions
Summary
Variational inequality theory has been studied widely in several branches of pure and applied sciences. Recall that a mapping T : C ® C is said to be L-Lipschitzian if there exists a constant L >0 such that. A mapping F : C ® X is said to be strongly accretive if there exists a constant h > 0 and j(x - y) Î J(x - y) such that. Let H be a real Hilbert space, whose inner product and norm are denoted by〈·, ·〉 and ||·||, respectively. Let A be a strongly positive bounded linear operator on H, that is, there exists a constant γ > 0 such that. A typical problem is to minimize a quadratic function over the set of the fixed points of a nonex-pansive mapping on a real Hilbert space H. where C is the fixed point set of a nonexpansive mapping T on H and u is a given point in H. Where F is a -Lipschitzian and h-strongly monotone operator with constants , h > 0 and
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