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A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces
摘要
The purpose of this research is to modify Halpern iteration's process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.
延伸閱讀
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- Wangkeeree, R., & Wangkeeree, R. (2009). The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces. Abstract and Applied Analysis, 2009(), 739-764. https://doi.org/10.1155/2009/624798
- Kimura, Y., & Nakajo, K. (2014). Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces. Journal of Applied Mathematics, 2014(), 791-800-287. https://doi.org/10.1155/2014/346517
- Zegeye, H., & Shahzad, N. (2013). Extragradient Method for Solutions of Variational Inequality Problems in Banach Spaces. Abstract and Applied Analysis, 2013(), 442-449-1144. https://doi.org/10.1155/2013/832548
- Zegeye, H., & Shahzad, N. (2012). An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces. Journal of Applied Mathematics, 2012(), 1189-1207-380. https://doi.org/10.1155/2012/504503