×

On soft quasi-pseudometric spaces. (English) Zbl 1477.54010

Summary: 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.

MSC:

54A40 Fuzzy topology
54E35 Metric spaces, metrizability
54E15 Uniform structures and generalizations
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] 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 · Zbl 1119.03050 · doi:10.1016/j.ins.2006.12.008
[2] 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 · doi:10.1007/s00521-011-0722-3
[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 · Zbl 0074.17802 · doi:10.2140/pjm.1956.6.405
[4] 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 · Zbl 1186.03068 · doi:10.1016/j.camwa.2008.11.009
[5] 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 · Zbl 1347.54058 · doi:10.1186/s13663-016-0502-y
[6] 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 · Zbl 0879.92003 · doi:10.1006/aama.1996.0503
[7] P. Fletcher and W. F. Lindgren, Quasi-uniform Spaces. Marcel Dekker, New York (1982). · Zbl 0501.54018
[8] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5 · Zbl 0936.03049 · doi:10.1016/S0898-1221(99)00056-5
[9] J. R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helvetici 39 (1964), 439-447. https://doi.org/10.1007/BF02566944 · Zbl 0151.30205 · doi:10.1007/BF02566944
[10] 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 · Zbl 1002.54002 · doi:10.1007/978-94-017-0470-0_3
[11] 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 · Zbl 1257.54040 · doi:10.1155/2012/765903
[12] 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 · Zbl 1245.54023 · doi:10.1016/j.topol.2011.02.016
[13] O. Olela Otafudu, Convexity in quasi-metric spaces, PhD thesis, University of Cape Town (2012). · Zbl 1285.54019
[14] 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 · Zbl 1365.54011 · doi:10.4995/agt.2017.5818
[15] S. Das and S. K. Samanta, Soft real sets, soft real numbers and their properties, J. Fuzzy Math. 20 (2012), 551-576. · Zbl 1271.03072
[16] S. Das and S. K. Samanta, Soft metric, Ann Fuzzy Math. Inform. 6 (2013), 77-94. · Zbl 1302.54014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.