System of generalized nonlinear variational-like inequalities and nearly asymptotically nonexpansive mappings: graph convergence and fixed point problems. (English) Zbl 1504.47095
Summary: In this paper, with the goal of investigating the problem of finding a common element of the set of fixed points of a nearly asymptotically nonexpansive mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities, an iterative algorithm is proposed. The notions of graph convergence and \(P-\eta\)-proximal point mapping are used and a new equivalence relationship between graph convergence and proximal-point mappings convergence of a sequence of lower semicontinuous and \(\eta\)-subdifferentiable proper functionals is established. Finally, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the two sets mentioned above are demonstrated.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
Keywords:
system of generalized nonlinear variational-like inequalities; \(P-\eta\)-proximal mapping; fixed point problem; nearly asymptotically nonexpansive mapping; graph convergence; iterative algorithm; strong convergenceReferences:
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