Abstract
Abstract In this paper, we prove a strong convergence theorem for finding a common solution of a general system of finite variational inequalities for finite different inverse-strongly accretive operators and solutions of fixed point problems for a nonexpansive semigroup in a Banach space based on a viscosity approximation method by using weak contraction mappings. Moreover, we can apply the above results to find the solutions of the class of k-strictly pseudocontractive mappings and apply a general system of finite variational inequalities into a Hilbert space. The results presented in this paper extend and improve the corresponding results of Ceng et al. (2008), Katchang and Kumam (2011), Wangkeeree and Preechasilp (2012), Yao et al. (2010) and many other authors. MSC:47H05, 47H10, 47J25.
Highlights
Let E be a real Banach space with norm · and C be a nonempty closed convex subset of E
By the following general system of variational inequalities, we extend into the general system of finite variational inequalities which is to find (x*, x*, . . . , x*M) ∈ C × C × · · · × C and is defined by λMAMx*M + x* – x*M, j(x – x* ) ≥, ∀x ∈ C λM– AM– x*M– + x*M – x*M, j(x – x*M) ≥, λ A x* + x* – x*, j(x – x* ) ≥, ∀x ∈ C, λ A x* + x* – x*, j(x – x* ) ≥, ∀x ∈ C
In this paper, motivated and inspired by the idea of Ceng et al [ ], Katchang and Kumam [ ] and Yao et al [ ], we introduce a new iterative scheme with weak contraction for finding solutions of a new general system of finite variational inequalities ( . ) for finite different inverse-strongly accretive operators and solutions of fixed point problems for nonexpansive semigroups in a Banach space
Summary
Let E be a real Banach space with norm · and C be a nonempty closed convex subset of E. In , Aoyama et al [ ] first considered the following generalized variational inequality problem in a smooth Banach space. [ ] first considered the following new general system of variational inequalities in Banach spaces: Let A : C → E be a β-inverse strongly accretive mapping. ). In this paper, motivated and inspired by the idea of Ceng et al [ ], Katchang and Kumam [ ] and Yao et al [ ], we introduce a new iterative scheme with weak contraction for finding solutions of a new general system of finite variational inequalities ) for finite different inverse-strongly accretive operators and solutions of fixed point problems for nonexpansive semigroups in a Banach space. The results presented in this paper extend and improve the corresponding results of Ceng et al [ ], Katchang and Kumam [ ], Wangkeeree and Preechasilp [ ], Yao et al [ ] and many other authors
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