On cyclic relatively nonexpansive mappings in generalized semimetric spaces

Moosa Gabeleh

Iran, Islamic Republic of

Ayatollah Boroujerdi University ; Institute for Research in Fundamental Sciences (IPM)

Department of Mathematics

Submitted: 2014-05-21

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Accepted: 2015-06-21

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Published: 2015-10-01

DOI: https://doi.org/10.4995/agt.2015.2988
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Keywords:

Cyclic relatively nonexpansive mapping, seminormal structure, generalized semimetric space

Supporting agencies:

This research was not funded

Abstract:

In this article, we prove a fixed point theorem for cyclic relatively nonexpansive mappings in the setting of generalized semimetric spaces by using a geometric notion of seminormal structure and then we conclude some results in uniformly convex Banach spaces. We also discuss on the stability of seminormal structure in generalized semimetric spaces.
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References:

L. M. Blumenthal,Theory and applications of distance geometry, Oxford Univ. Press, London (1953).

M. S. Brodskii and D. P. Milman,On the center of a convex set, Dokl. Akad. Nauk. USSR 59(1948), 837-840 (in Russian). M. Gabeleh, Minimal sets of noncyclic relatively nonexpansive mappings in convex metric spaces, Fixed Point Theory, to appear.

A. A. Eldred, W. A. Kirk and P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171(2005), 283-293. https://doi.org/10.4064/sm171-3-5

R. Espínola, A new approach to relatively nonexpansive mappings, Proc. Amer. Math. Soc. 136(2008), 1987-1996. https://doi.org/10.1090/S0002-9939-08-09323-4

R. Espínola and M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numer. Funct. Anal. Optim. 34 (2013), 845-860. https://doi.org/10.1080/01630563.2013.763824

M. Gabeleh and N. Shahzad, Seminormal structure and fixed points of cyclic relatively nonexpansive mappings, Abstract Appl. Anal. 2014 (2014), Article ID 123613, 8 pages. https://doi.org/10.1155/2014/123613

W. A. Kirk,A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006. https://doi.org/10.2307/2313345

W. A. Kirk and B. G. Kang, A fixed point theorem revisited, J. Korean Math. Soc. 34(1997), 285-291.

W. A. Kirk, P. S. Srinivasan and P. Veeramani, Fixed points for mappings satisfying cyclic contractive conditions, Fixed Point Theory 4, no. 1 (2003), 79-86.

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