An Explicit Midpoint Algorithm for Nonexpansive Semigroup in smooth Banach Spaces

محورهای موضوعی : Fixed Point Theory and its Applications

Hamid Sahebi ¹ (Department of Mathematics, Ashtian Branch, Islamic Azad university, Ashtian, Iran.)
Andreea Fulga ² (Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Universitatea Transilvania Brasov, Brasov, Romania.)

تاریخ دریافت : 1400/12/27 تاریخ پذیرش : 1400/12/28 تاریخ انتشار : 1400/02/11

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

چکیده مقاله :

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.