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On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems

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Abstract

Our aim is introduce a new class of procedures, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures). Then by a UAR-procedure we prove the convergence of two explicit iterative methods to the unique solution of a variational inequality problem on the set of common fixed points of a family of mappings, in the setting of Hilbert spaces.

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Acknowledgments

The authors are extremely grateful to the anonymous referees for their useful comments and suggestions.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá della Calabria, 87036 , Arcavacata di Rende, CS, Italy

    Giuseppe Marino & Luigi Muglia

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  1. Giuseppe Marino
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  2. Luigi Muglia
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Correspondence to Giuseppe Marino.

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Marino, G., Muglia, L. On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems. Optim Lett 9, 263–282 (2015). https://doi.org/10.1007/s11590-013-0705-7

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