An Explicit Midpoint Algorithm for Nonexpansive Semigroup in smooth Banach Spaces

Subject Areas : Fixed Point Theory and its Applications

Hamid Sahebi ^{1 *} , Andreea Fulga ²

1 - Department of Mathematics, Ashtian Branch, Islamic Azad university, Ashtian, Iran.
2 - Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Universitatea Transilvania Brasov, Brasov, Romania.

Received: 2022-03-18 Accepted : 2022-03-19 Published : 2021-05-01

Keywords: smooth Banach space, Non-expansive semigroup, fixed point, equilibrium problem, midpoint method,

Abstract :

In this paper, we introduce a new iterative midpoint rule for finding a solutionof fixed point problem for a non-expansive semigroup in smooth Banach spaces. Weestablish a strong convergence theorem for the sequences generated by our proposediterative scheme. A numerical example present to illustrate the convergenceresult. Our results improve and extend the corresponding results in the literature.