Fixed point, convergence and nonlinear ergodic theorems for some semigroups in Hilbert spaces, By Hossein Piri

Research

Title	Fixed point, convergence and nonlinear ergodic theorems for some semigroups in Hilbert spaces
Type	Article
Keywords	Convergence theorem, nonlinear ergodic theorem, banach limit, invariant mean.
Researchers	Hossein Piri، Bayaz Daraby، Asghar Rahimi، Mostafa Ghasemi

Abstract

In this paper, we first introduce some semigroups of mappings called quasi-nonexpansive, nonspreading, hybrid, TJ-1, TJ-2, and generalized hybrid semigroup. Then, using the theory of invariant means, we prove fixed point theorems, weak convergence theorem of Mann’s type and generalized nonlinear ergodic theorem for such semigroups in a Hilbert space. Furthermore, we prove a strong convergence theorem of Halpern’s type for the proposed semigroups in a Hilbert space. The results presented in this paper mainly extend and improved some wellknown results in the literature.