Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 9, Number 2 (2018), 220-232.
On generalized pointwise noncyclic contractions without proximal normal structure
In this article, we introduce a new class of noncyclic mappings called generalized pointwise noncyclic contractions, and we prove a best proximity pair theorem for this class of noncyclic mappings in the setting of strictly convex Banach spaces. Our conclusions generalize a result due to Kirk and Royalty. We also study convergence of iterates of noncyclic contraction mappings in uniformly convex Banach spaces.
Ann. Funct. Anal. Volume 9, Number 2 (2018), 220-232.
Received: 22 December 2016
Accepted: 16 May 2017
First available in Project Euclid: 7 December 2017
Permanent link to this document
Digital Object Identifier
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 46B20: Geometry and structure of normed linear spaces
Gabeleh, Moosa. On generalized pointwise noncyclic contractions without proximal normal structure. Ann. Funct. Anal. 9 (2018), no. 2, 220--232. doi:10.1215/20088752-2017-0049. https://projecteuclid.org/euclid.afa/1512637231