Fixed Point and Convergence Theorems for Two Nonlinear Mappings in Hilbert Spaces (Nonlinear Analysis and Convex Analysis)

Abstract

In this paper, first, we introduce attractive point and fixed point theorems and mean convergence theorem for two commutative 2-generalized mappings in Hilbert spaces. Next we obtain a weak convergence theorem of Mann s type iteration, a strong convergence theorem of Halpern's type iteration, and a strong convergence theorem by the hybrid method for two commutative 2-generalized hybrid mappings in a Hilbert space.