On fixed point theorems involving altering distances in Menger probabilistic metric spaces

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Došenović T., Kumam P., Gopal D., Patel D.K., Takači A.

Publisher: SpringerOpen

Publication year: 2013

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2013

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84897659405&doi=10.1186%2f1029-242X-2013-576&partnerID=40&md5=ee09c141eef0b82027b76eaa8efae493

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we show by means of an example that the results of Babačev (Appl. Anal. Discrete Math. 6:257-264, 2012) do not hold for the class of t-norms T ≤ Tp. Further, we prove a fixed point theorem for quasi-type contraction involving altering distance functions which is weaker than that proposed by Babačev but for any continuous t-norm in a complete Menger space. ©2013 Došenović et al.; licensee Springer.

Keywords

Continuous t-norm, Menger PM-spaces