Let K be a nonempty closed convex subset of a Banach space E and T : K → K be a nonexpansive mapping. Using a viscosity approximation method, we study the implicit midpoint rule of a nonexpansive mapping T. We establish a strong convergence theorem for an iterative algorithm in the framework of uniformly smooth Banach spaces and apply our result to obtain the solutions of an accretive mapping and a variational inequality problem. The numerical example which compares the rates of convergence shows that the iterative algorithm is the most efficient. Our result is unique and the method of proof is of independent interest.
Aibinu, M. (2019). The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space. Afribary. Retrieved from https://afribary.com/works/the-implicit-midpoint-rule-of-nonexpansive-mappings-and-applications-in-uniformly-smooth-banach-spaces-1537512546
Aibinu, Mathew "The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space" Afribary. Afribary, 29 Jul. 2019, https://afribary.com/works/the-implicit-midpoint-rule-of-nonexpansive-mappings-and-applications-in-uniformly-smooth-banach-spaces-1537512546. Accessed 30 Apr. 2024.
Aibinu, Mathew . "The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space". Afribary, Afribary, 29 Jul. 2019. Web. 30 Apr. 2024. < https://afribary.com/works/the-implicit-midpoint-rule-of-nonexpansive-mappings-and-applications-in-uniformly-smooth-banach-spaces-1537512546 >.
Aibinu, Mathew . "The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space" Afribary (2019). Accessed April 30, 2024. https://afribary.com/works/the-implicit-midpoint-rule-of-nonexpansive-mappings-and-applications-in-uniformly-smooth-banach-spaces-1537512546