On the system of nonlinear mixed implicit equilibrium problems in Hilbert spaces. (English) Zbl 1184.49003

Summary: We use the Wiener-Hopf equations and the Yosida approximation notions to prove an existence theorem of a System of nonlinear Mixed Implicit Equilibrium (SMIE) problems in Hilbert spaces. The algorithm for finding a solution of the problem SMIE is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.


49J27 Existence theories for problems in abstract spaces
49M30 Other numerical methods in calculus of variations (MSC2010)
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