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arXiv · 1403.3204

Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems

Ibrahim Karahan·Murat Ozdemir
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Abstract

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality for an inverse strongly monotone mapping in a Hilbert space. Using this process, we prove a weak convergence theorem for the class of nonexpansive mappings in Hilbert spaces. Finally, as an application, we give some theorems by using resolvent operator and strictly pseudocontractive mapping.

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BibTeXRIS

Ibrahim Karahan, Murat Ozdemir. 2014-03-13. Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems. https://arxiv.org/abs/1403.3204

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