IJPAM: Volume 115, No. 3 (2017)

Title

COMMON FIXED POINT AND BEST PROXIMITY POINT
THEOREMS IN C*-ALGEBRA-VALUED METRIC SPACES

Authors

Saranan Mondal$^1$, Ankush Chanda$^2$, Surajit Karmakar$^3$
$^{1,2,3}$Department of Mathematics
National Institute of Technology
Durgapur, West Bengal, INDIA

Abstract

In the article, we prove the existence and uniqueness of common fixed points for self-maps with contractive or expansive conditions on $C^*$-algebra-valued metric spaces without taking the continuity assumption on either of the mappings $S$ or $T$. Also, we define $C^*$-algebra-valued proximal contraction and show the existence and uniqueness of best proximity points for these proximal contraction mappings on the said spaces. Moreover, the paper provides an application to prove the existence and uniqueness of the solution for a type of integral equations.

History

Received: December 14, 2016
Revised: March 23, 2017
Published: July 27, 2017

AMS Classification, Key Words

AMS Subject Classification: $C^*$-algebra-valued metric space, expansion mapping, $C^*$-algebra-valued proximal contraction, common fixed point, best proximity point
Key Words and Phrases: 47H10, 54H25

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v115i3.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 3
Pages: 477 - 496


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