Strong convergence theorems for fixed point problems of infinite family of asymptotically quasi-\(\phi\)-nonexpansive mappings and a system of equilibrium problems. (English) Zbl 1478.47092
Summary: In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of infinite family of asymptotically quasi-\(\phi\)-nonexpansive mappings and of the set of solutions for finite equilibrium problems in a real Banach space. Our results are the generalization of the results [Y. Shehu, Comput. Math. Appl. 63, No. 6, 1089–1103 (2012; Zbl 1247.65075); J. K. Kim, Fixed Point Theory Appl. 2011, Paper No. 10, 15 p. (2011; Zbl 1390.47020); with N. Buong, ibid. 2011, Article ID 780764, 15 p. (2011; Zbl 1221.65153)], and an improvement of the result in [L. Yang et al., Appl. Math. Comput. 218, No. 10, 6072–6082 (2012; Zbl 1246.65086)].
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
common fixed point; asymptotically quasi-\(\phi\)-nonexpansive mappings; equilibrium problems; generalized \(f\)-projection operatorReferences:
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