A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings

Ravi P. Agarwal; Ebrahim Soori; Donal O'Regan

A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings

Functional Analysis 2021-04-27 v5

Authors: Ravi P. Agarwal , Ebrahim Soori , Donal O'Regan

Abstract

In this paper, a simple proof is presented for the convergence of the algorithms for the class of relaxed $(u, v)$ -cocoercive mappings and $\alpha$ -inverse strongly monotone mappings. Based on $\alpha$ -expansive maps, for example, a simple proof of the convergence of the recent iterative algorithms by relaxed $(u, v)$ -cocoercive mappings due to Kumam-Jaiboon is provided. Also a simple proof for the convergence of the iterative algorithms by inverse-strongly monotone mappings due to Iiduka-Takahashi in a special case is provided. These results are an improvement as well as a refinement of previously known results.

Keywords

relaxed (u,v)-cocoercive mappings alpha-inverse strongly monotone mappings convergence iterative algorithms alpha-expansive maps

Cite

@article{arxiv.1802.02726,
  title  = {A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings},
  author = {Ravi P. Agarwal and Ebrahim Soori and Donal O'Regan},
  journal= {arXiv preprint arXiv:1802.02726},
  year   = {2021}
}

Comments

7 pages. Accepted and under publishing in the International Journal of Nonlinear Analysis and Applications (IJNAA)

A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings

Abstract

Keywords

Cite

Comments

Related papers