Existence and algorithm of solutions for nonlinear mixed variational-like inequalities in Banach spaces.
A new class of nonlinear mixed variational-like inequalities in reflexive Banach spaces is introduced. It extends previous results obtained in Hilbert spaces by \textit{X. P. Ding} [J. Sichuan Norm. Univ., Nat. Sci. 22, No. 5, 494--503 (1999; Zbl 0965.49010)], \textit{N. J. Huang} and \textit{C. X. Deng} [J. Math. Anal. Appl. 256, 345--359 (2001; Zbl 0972.49008)]. The existence and the uniqueness of the solution is proved by applying a minimax inequality due to the author. By using a new auxiliary variational-like inequality technique, a general iterative algorithm to compute approximate solutions is developed. A convergence criterion of that algorithm is also given.
nonlinear mixed variational-like inequality
scientific article; zbMATH DE number 1970755
scientific article