Parallel hybrid viscosity method for fixed point problems, variational inequality problems and split generalized equilibrium problems

Abstract

Abstract In this paper, we first propose a new parallel hybrid viscosity iterative method for finding a common element of three solution sets: (i) finite split generalized equilibrium problems; (ii) finite variational inequality problems; and (iii) fixed point problem of a finite collection of demicontractive operators. And we prove that the sequence generated by the iterative scheme strongly converges to a common solution of the above-mentioned problems. Also, we present numerical examples to demonstrate the effectiveness of our algorithm. Our results presented in this paper improve and extend many recent results in the literature.

Keywords

• Split generalized equilibrium problems
• Variational inequality problems
• Fixed point problems
• Parallel hybrid viscosity method
• Lipschitzian mappings