Some Common Fixed-Point Theorems in Fuzzy Metric Space in the Context of Single and Set-Valued Mapping via OWC Mapping

Authors

  • Sushma Yadav Department of Mathematics, Government Narmada P.G. College (affiliated to Barkatullah University), Narmadapuram 461001, Madhya Pradesh, India https://orcid.org/0009-0002-0415-8166
  • Kamal Wadhwa Department of Mathematics, Government Narmada P.G. College (affiliated to Barkatullah University), Narmadapuram 461001, Madhya Pradesh, India https://orcid.org/0000-0002-1889-9611
  • Rashmi Tiwari Department of Mathematics, Government M.G.M. P.G. College (affiliated to Barkatullah University), Itarsi, Narmadapuram 461111, Madhya Pradesh, India https://orcid.org/0009-0001-1156-3322

DOI:

https://doi.org/10.26713/cma.v16i1.2963

Keywords:

Fuzzy Metric Space (FMS), Common Fixed Point (CFP), Occasionally Weakly Compatible Mapping (OWC), Single Valued Mapping (SVM), Set-Valued Mapping (SEVM)

Abstract

 This study aims to construct some common theorems in FMS for two pairs of single and set-valued OCM mappings that satisfy integral type contractive requirements. Our findings expand upon and generalize a number of related findings from previous research for independent of continuity and completeness.

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References

M. E. Abd El-Monsef, H. M. Abu-Donia and K. Abd-Rabou, Common fixed point theorems of single and set-valued mappings on 2-metric spaces, Applied Mathematics & Information Sciences 1(2) (2007), 185 – 194, URL: https://www.naturalspublishing.com/download.asp?ArtcID=195.

R. Arora and M. Kumar, Unique fixed point theorems for α-ψ-contractive type mappings in fuzzy metric space, Cogent Mathematics 3(1) (2016), 1183286, DOI: 10.1080/23311835.2016.1183286.

A. Azam, Fuzzy fixed points of fuzzy mappings via a rational inequality, Hacettepe Journal of Mathematics and Statistics 40(3) (2011), 421 – 431, URL: https://dergipark.org.tr/tr/download/article-file/86583.

C. D. Bari and C. Vetro, Common fixed point theorems for weakly compatible maps satisfying a general contractive condition, International Journal of Mathematics and Mathematical Sciences 2008(1) (2008), 891375, DOI: 10.1155/2008/891375.

R. Bhardwaj, S. Singh, S. Gupta and V. K. Sharma, Common fixed point theorems on compatibility and continuity in soft metric spaces, Communications in Mathematics and Applications 12(4) (2021), 951 – 968, DOI: 10.26713/cma.v12i4.1657.

H. Bouhadjera and A. Djoudi, Common fixed point theorems for single and set valued maps without continuity, Analele Stiintifice ale Universitatii Ovidius Constanta 16(1) (2008), 49 – 58.

H. Bouhadjera and A. Djoudi, Common fixed point theorems for single and set-valued maps satisfying a strict contractive condition, Mathematical Communications 13(1) (2008), 27 – 32, URL: https://core.ac.uk/download/pdf/14396447.pdf.

S. Chauhan, S. Bhatnagar and S. Radenovic, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Le Matematiche 68(1) (2013), 87 – 98, DOI: 10.4418/2013.68.1.8.

A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64(3) (1994), 395 – 399, DOI: 10.1016/0165-0114(94)90162-7.

S. Gupta, R. Bhardwaj, B. R. Wadkar and R. M. Sharraf, Fixed point theorems in fuzzy metric spaces, Materials Today: Proceedings 29(Part 2) (2020), 611 – 616, DOI: 10.1016/j.matpr.2020.07.322.

V. Gupta, R. K. Saini and M. Verma, Fixed point theorems for single valued α-ψ-mappings in fuzzy metric spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68(1) (2018), 392 – 400, DOI: 10.31801/cfsuasmas.424203.

S. Hong and Y. Peng, Fixed points of fuzzy contractive set-valued mappings and fuzzy metric completeness, Fixed Point Theory and Applications 2013 (2013), Article number: 276, DOI: 10.1186/1687-1812-2013-276.

P. Jain, V. Jat and U. Singh, Transformations and solutions of integral equation involving Bessel Maitland function, Journal of Algebraic Statistics 13(2) (2022), 1541 – 1548, URL: https://publishoa.com/index.php/journal/article/view/323.

C. Jinakul, A. Wiwatwanich and A. Kaewkhao, Common fixed point theorem for multi-valued mappings on b-metric spaces, International Journal of Pure and Applied Mathematics 113(1) (2017), 167 – 179, DOI: 10.12732/ijpam.v113i1.15.

J. M. Joseph, D. D. Roselin and M. Marudai, Fixed point theorems on multi valued mappings in b-metric spaces, SpringerPlus 5 (2016), Article number: 217, DOI: 10.1186/s40064-016-1870-9.

S. Kanwal, A. Ali, A. Al Mazrooei and G. S. Garcia, Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces, AIMS Mathematics 8(5) (2023), 10095 – 10112, DOI: 10.3934/math.2023511.

S. Kanwal, M. S. Shagari, H. Aydi, A. Mukheimer and T. Abdeljawad, Common fixed-point results of fuzzy mappings and applications on stochastic Volterra integral equations, Journal of Inequalities and Applications 2022 (2022), Article number: 110, DOI: 10.1186/s13660-022-02849-2.

I. Kramosil and J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika 11(5) (1975), 336 – 344, URL: https://www.kybernetika.cz/content/1975/5/336/paper.pdf.

S. Kumar and B. Fisher, A common fixed point theorem in fuzzymetric space using property (e.a.) and implicit relation, Thai Journal of Mathematics 8(3) (2010), 439 – 446, URL: https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/212/208.

P. P. Murthy, S. Kumar and K. Tas, Common fixed points of self maps satisfying an integral type of contractive condition in fuzzy metric spaces, Mathematical Communications 15(2) (2010), 521 – 537, URL: https://hrcak.srce.hr/file/92657.

R. Namdev, R. Tiwari, U. Singh and R. Bhardwaj, Common fixed-point theorems for rational expression in fuzzy metric space using E.A. like property, African Journal of Biological Sciences 6(10) (2024), 6224 – 6237, URL: https://www.afjbs.com/uploads/paper/e21410612f9c89f053adb4974e72bb7d.pdf.

K. P. R. Rao, K. R. K. Rao and S. Sedghı, Common coupled fixed point theorems in fuzzy metric spaces, Gazi University Journal of Science 27(2) (2014), 739 – 745, URL: https://dergipark.org.tr/en/pub/gujs/issue/7431/97740.

S. Rezapour, M. E. Samet, Some fixed-point results for α-ψ-contractive type mappings on intuitionistic fuzzy metric space, Journal of Advanced Mathematical Studies 7(1) (2014), 176 – 181.

T. K. Samanta and M. Mohinta, Common fixed point theorems for single and set-valued maps in non-Archimedean fuzzy metric spaces, Acta Universitatis Sapientiae, Mathematica 4(2) (2012), 132 – 144, URL: https://www.emis.de/journals/AUSM/C4-2/math42-3.pdf.

K. P. R. Sastry, M. V. R. Kameswari, C. S. Rao and R. V. Bhaskar, Banach type fixed point theorem for set valued maps on a fuzzy metric space, General Mathematics Notes 23(1) (2014), 32 – 44, URL: https://www.emis.de/journals/GMN/volumes/all_volumes_2014.html.

U. Singh, N. Singh, R. Singh and R. Bhardwaj, Common invariant point theorem for multivalued generalized fuzzy mapping in b-metric space, in: Recent Trends in Design, Materials and Manufacturing, Lecture Notes in Mechanical Engineering series, Springer, Singapore, pp. 23 – 35, (2022), DOI: 10.1007/978-981-16-4083-4_3.

Sonam, R. Bhardwaj and S. Narayan, Fixed point results in soft fuzzy metric spaces, Mathematics 11(14) (2023), 3189, DOI: 10.3390/math11143189.

Sonam, V. Rathore, A. Pal, R. Bhardwaj and S. Narayan, Fixed-point results for mappings satisfying implicit relation in orthogonal fuzzy metric spaces, Advances in Fuzzy Systems 2023 (2023), Article ID 5037401, DOI: 10.1155/2023/5037401.

K. Wadhwa, H. Dubey and R. Jain, Impact of “E.A. Like” property on common fixed point theorems in fuzzy metric spaces, Journal of Advanced Studies in Topology 3(1) (2012), 52 – 59.

L. A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.

L. A. Zadeh, G. J. Klir and B. Yuan, Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers, Vol. 6, World Scientific, 840 pages (1996), DOI: 10.1142/2895.

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Published

31-07-2025
CITATION

How to Cite

Yadav, S., Wadhwa, K., & Tiwari, R. (2025). Some Common Fixed-Point Theorems in Fuzzy Metric Space in the Context of Single and Set-Valued Mapping via OWC Mapping. Communications in Mathematics and Applications, 16(1), 1–14. https://doi.org/10.26713/cma.v16i1.2963

Issue

Vol. 16 No. 1 (2025)

Section

Research Article

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