Abstract
The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △-convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT0 spaces and Hilbert spaces as special cases.
Highlights
The iterative methods for approximating fixed points of nonexpansive mappings have received a great attention due to the fact that in many practical problems, the controlling operators are nonexpansive
There has been no change to the content of the article
This change was necessary for the journal to transition from the previous publisher to the new one
Summary
The iterative methods for approximating fixed points of nonexpansive mappings have received a great attention due to the fact that in many practical problems, the controlling operators are nonexpansive (cf. [16]). An implicit iterative method was proposed [25] and studied in [7,12]. Published in the Arab Journal of Mathematical Sciences. The publisher wishes to inform readers that the article “The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces” was originally published by the previous publisher of the Arab Journal of Mathematical Sciences and the pagination of this article has been subsequently changed. There has been no change to the content of the article This change was necessary for the journal to transition from the previous publisher to the new one. To access and cite this article, please use Fukhar-ud-din, H., Khan, A.R. (2019), “The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces” Arab Journal of Mathematical Sciences, Vol 26 No 1/2, pp. The original publication date for this paper was 22/02/2019
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