TY - JOUR
T1 - Construction of a common solution of a finite family of variational inequality problems for monotone mappings
AU - Alghamdi, Mohammed Ali
AU - Shahzad, Naseer
AU - Zegeye, Habtu
N1 - Publisher Copyright:
© 2016 All rights reserved.
PY - 2016
Y1 - 2016
N2 - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ai: C → H, for i = 1, 2; be two Li-Lipschitz monotone mappings and let f: C → C be a contraction mapping. It is our purpose in this paper to introduce an iterative process for finding a point in V I(C,A1) ∩ V I(C, A2) under appropriate conditions. As a consequence, we obtain a convergence theorem for approximating a common solution of a finite family of variational inequality problems for Lipschitz monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
AB - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ai: C → H, for i = 1, 2; be two Li-Lipschitz monotone mappings and let f: C → C be a contraction mapping. It is our purpose in this paper to introduce an iterative process for finding a point in V I(C,A1) ∩ V I(C, A2) under appropriate conditions. As a consequence, we obtain a convergence theorem for approximating a common solution of a finite family of variational inequality problems for Lipschitz monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
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U2 - 10.22436/jnsa.009.04.21
DO - 10.22436/jnsa.009.04.21
M3 - Article
AN - SCOPUS:84955618962
SN - 2008-1898
VL - 9
SP - 1645
EP - 1657
JO - Journal of Nonlinear Science and Applications
JF - Journal of Nonlinear Science and Applications
IS - 4
ER -