FIXED POINT AND NONLINEAR ERGODIC THEOREMS FOR SOME NEW TYPE SEMIGROUPS OF MAPPINGS, By Hossein Piri

Research

Title	FIXED POINT AND NONLINEAR ERGODIC THEOREMS FOR SOME NEW TYPE SEMIGROUPS OF MAPPINGS
Type	Article
Keywords	Fixed point theorem, generalized nonlinear ergodic theorem, nonspreading retraction, convergence theorem
Researchers	Hossein Piri، Mostafa Ghasemi

Abstract

In the present paper, some new type of semigroups of mappings are introduced. Then, by using the theory of invariant means, fixed point theorem, and existence of nonspreading retraction for these semigroup are deduced and the illustrative examples are given. Also, weak convergence theorem of Mann’s type, generalized Baillon’s nonlinear ergodic theorem and strong convergence theorem of Halpern’s type for such semigroups in the Hilbert space are considered. At the end, some applications are investigated.