Nonlinear Operators of Monotone Type and Convergence Theorems with Equilibrium Problems in Banach Spaces
Wataru Takahashi, Jen‐Chih Yao · Taiwanese Journal of Mathematics · 2011
Our purpose in this paper is first to discuss nonlinear operators and nonlinear projections in Banach spaces which are related to the resolvents of $m$-accretive operators and maximal monotone operators. Some of these operators in Banach spaces are new. Next, we discuss some properties for such nonlinear operators and nonlinear projections in Banach spaces. Further, using these properties, we prove strong convergence theorems by hybrid methods for nonlinear operators with equilibrium problems in Banach spaces.