Strong convergence theorems for a countable family of quasi-Lipschitzian mappings and its applications |
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| Authors: | Weerayuth Nilsrakoo |
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| Institution: | a Department of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani 34190, Thailand
b Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand |
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| Abstract: | We use the hybrid method in mathematical programming to obtain strong convergence to common fixed points of a countable family of quasi-Lipschitzian mappings. As a consequence, several convergence theorems for quasi-nonexpansive mappings and asymptotically κ-strict pseudo-contractions are deduced. We also establish strong convergence of iterative sequences for finding a common element of the set of fixed point, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain the corresponding results due to Tada-Takahashi and Nakajo-Shimoji-Takahashi. |
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| Keywords: | Strong convergence theorem Quasi-Lipschitzian mapping Equilibrium problem Variational inequality problem |
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