On soft quasi-pseudometric spaces

Hope Sabao; Olivier Olela Otafudu

doi:10.4995/agt.2021.13084

Authors

Hope Sabao University of the Witwatersrand
Olivier Olela Otafudu University of the Western Cape https://orcid.org/0000-0001-9593-7899

DOI:

https://doi.org/10.4995/agt.2021.13084

Keywords:

soft-metric, soft-quasi-pseudometric, soft Isbell convexity

Abstract

In this article, we introduce the concept of a soft quasi-pseudometric space. We show that every soft quasi-pseudometric induces a compatible quasi-pseudometric on the collection of all soft points of the absolute soft set whenever the parameter set is finite. We then introduce the concept of soft Isbell convexity and show that a self non-expansive map of a soft quasi-metric space has a nonempty soft Isbell convex fixed point set.

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Author Biographies

Hope Sabao, University of the Witwatersrand

School of Mathematics

Post Doc

Olivier Olela Otafudu, University of the Western Cape

Department of Mathematics and Applied Mathematics

References

H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci. 177 (2007), 2226-2735. https://doi.org/10.1016/j.ins.2006.12.008

A. Aygünoglu and H. Aygün, Some notes on soft topological spaces, Neural. Comput. Appl. 21 (2012), 113-119. https://doi.org/10.1007/s00521-011-0722-3

N. Aronszajn and P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439. https://doi.org/10.2140/pjm.1956.6.405

M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009

M. Abbas, G. Murtaza and S. Romaguera, On the fixed point theory of soft metric spaces. Fixed Point Theory Appl. 2016, 17 (2016). https://doi.org/10.1186/s13663-016-0502-y

A. Dress, V. Moulton and M. Steel, Trees, taxonomy and strongly compatible multi-state characters, Adv. Appl. Math. 71 (1997), 1-30. https://doi.org/10.1006/aama.1996.0503

P. Fletcher and W. F. Lindgren, Quasi-uniform Spaces. Marcel Dekker, New York (1982).

D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5

J. R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helvetici 39 (1964), 439-447. https://doi.org/10.1007/BF02566944

H.-P. A. Künzi, Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, in: Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), vol. 3, Kluwer (Dordrecht, 2001), pp. 853-968. https://doi.org/10.1007/978-94-017-0470-0_3

H.-P. A Künzi and O. Olela Otafudu, q-Hyperconvexity in quasi-pseudometric spaces and fixed point theorems, J. Func. Spaces Appl. 2012 (2012), 765903. https://doi.org/10.1155/2012/765903

E. Kemajou, H.-P. A Künzi and O. Olela Otafudu, The Isbell-hull of a di-space. Topology Appl. 159 (2012), 2463-2475. https://doi.org/10.1016/j.topol.2011.02.016

O. Olela Otafudu, Convexity in quasi-metric spaces, PhD thesis, University of Cape Town (2012).

O. Olela Otafudu and H. Sabao, Set-valued contractions and q-hyperconvex spaces, J. Nonlinear Convex Anal. 18 (2017), 1609-1617. https://doi.org/10.4995/agt.2017.5818

S. Das and S. K. Samanta, Soft real sets, soft real numbers and their properties, J. Fuzzy Math. 20 (2012), 551-576.

S. Das and S. K. Samanta, Soft metric, Ann Fuzzy Math. Inform. 6 (2013), 77-94.