Convergence analysis of generalized iterative methods for some variational inequalities involving pseudomonotone operators in Banach spaces

Abstract

This work is concerned with the analysis of convergence of generalized iterative methods for solving some variational inequalities with pseudomonotone operators and convex nondifferentiable functionals in Banach spaces. Such inequalities occur, in particular, in descriptions of steady-state filtration processes and equilibrium problems for soft shells. The results obtained in this paper include and extend the results of B. Badriev et al. [I.B. Badriev, O.A. Zadvornov, A.M. Saddeek, Convergence analysis of iterative methods for some variational inequalities with pseudomonotone operators, Diff. Equ. 37 (7) (2001) 934–942].