Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces

• Main Authors: Panisa Lohawech, Anchalee Kaewcharoen, Ali Farajzadeh
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Online Access: http://dx.doi.org/10.1155/2021/9980309

In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.