## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 310106, 12 pages.

### Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

M. De la Sen

#### Abstract

This paper is devoted to investigating the limit properties of distances and the existence and uniqueness of fixed points, best proximity points and existence, and uniqueness of limit cycles, to which the iterated sequences converge, of single-valued, and so-called, contractive precyclic self-mappings which are proposed in this paper. Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. Each point of a subset is mapped either in some point of the same subset or in a point of the adjacent subset. In the general case, the contractive condition of contractive precyclic self-mappings is admitted to be point dependent and it is only formulated on a complete disposal, rather than on each individual subset, while it involves a condition on the number of iterations allowed within each individual subset before switching to its adjacent one. It is also allowed that the distances in-between adjacent subsets can be mutually distinct including the case of potential pairwise intersection for only some of the pairs of adjacent subsets.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 310106, 12 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807679

Digital Object Identifier
doi:10.1155/2013/310106

Mathematical Reviews number (MathSciNet)
MR3090613

Zentralblatt MATH identifier
1273.54050

#### Citation

De la Sen, M. Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings. J. Appl. Math. 2013, Special Issue (2013), Article ID 310106, 12 pages. doi:10.1155/2013/310106. https://projecteuclid.org/euclid.jam/1394807679

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