A new iterative algorithm for solving some nonlinear problems in Hilbert spaces

Abstract

In this paper, a new iterative algorithm for finding a common element of the set of minimizers of a convex function, the set of solutions of variational inequality problem, the set of solutions of equilibrium problems and the set of fixed points of demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. Our theorems are significant improvements in several important recent results.

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

“…For other important recent results regarding the study of VIP over the set of fixed points of demicontractive mappings and of finite families of demicontractive mappings, we refer to Maingé [22,103], Suantai and Phuengrattana [2], Thong and Hieu [104], Ogbuisi and Mewomo [105], Alakoya et al [106], Meddahi et al [107], Linh et al [108], Okeke et al [109,110], Rehman et al [111], Sow [112][113][114], Tan et al [115,116], Thong et al [117,118], Thong and Hieu [104,119], Amarachi Uzor et al [120], etc.…”