On the Best Proximity Points for p –Cyclic Summing Contractions

Miroslav Hristov, Atanas Ilchev and Boyan Zlatanov
Additional contact information
Miroslav Hristov: Department of Mathematical Analysis, Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, 115 Universitetska str., 9700 Shumen, Bulgaria
Atanas Ilchev: Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Assen str., 4000 Plovdiv, Bulgaria
Boyan Zlatanov: Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Assen str., 4000 Plovdiv, Bulgaria

Mathematics, 2020, vol. 8, issue 7, 1-11

Abstract: We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p –cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.

Keywords: fixed point; cyclical operator; contractive condition; best proximity point; uniformly convex Banach space; p –summing contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/7/1060/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/7/1060/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:7:p:1060-:d:378965

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().