Strong and Δ - Convergence Theorems using Modified Proximal Point Algorithm in CAt(0) Spaces

Volume 7 Issue 2 April - June 2018

Research Paper

Strong and Δ - Convergence Theorems using Modified Proximal Point Algorithm in CAt(0) Spaces

Apurva Kumar Das*, Shailesh Dhar Diwan**, Samir Dashputre***

* Lecturer, Department of Mathematics, Government Polytechnic Sukma, Chhattisgarh, India.

** Associate Professor, Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

*** Assistant Professor, Department of Mathematics, Government College Arjunda, Balod, Chhattisgarh, India.

Das. A.K., Diwan. S.D., and Dashputre. S. (2018). Strong and Δ - Convergence Theorems using Modified Proximal Point Algorithm in CAt(0) Spaces. i-manager’s Journal on Mathematics, 7(2), 8-16. https://doi.org/10.26634/jmat.7.2.13999

Abstract

Let (X, d) be a complete CAT(0) space and f∶ X → (-∞, ∞] be a proper convex and lower semi-continuous function. Suppose T be a nonexpansive mapping on X such that Ω=F(T) ⋂ argmin(yϵX) f(y) is nonempty. The purpose of this paper is to define a modified proximal point algorithm and prove the existence of a sequence proposed by the authors converges to Ω. In this paper, they prove strong and Δ-convergence theorems with their proposed modified proximal point algorithm in CAT(0) spaces.