Convergence Theorems by Using a Projection Method without the Monotonicity in Hilbert Spaces

Areerat Arunchai, Somyot Plubtieng, Thidaporn Seangwattana

Abstract

In this paper, we present a projection iterative algorithm for finding the common solution of variational inequality problem without monotonicity, fixed point problem of a nonexpansive mapping, and zero point problem of the sum of two monotone mappings in Hilbert spaces. When setting the solution set of the dual variational inequality is nonempty, the strong convegence theorem is established under some suitable control conditions. Finally, we reduce some mappings in our main result to study several problems.