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Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
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Education: PhD.
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Faculty: 1
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Research

Title
Fixed point, convergence and nonlinear ergodic theorems for some semigroups in Hilbert spaces
Type
JournalPaper
Keywords
Convergence theorem, nonlinear ergodic theorem, banach limit, invariant mean
Year
2020
Journal Journal of Fixed Point Theory and Applications
DOI
Researchers Hossein Piri ، Bayaz Daraby ، Asghar Rahimi ، Mostafa Ghasemi

Abstract

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.