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Compatible mappings and common fixed points

Author

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  • Gerald Jungck

Abstract

A generalization of the commuting mapping concept is introduced. Properties of this weakened commutativity are derived and used to obtain results which generalize a theorem by Park and Bae, a theorem by Hadzic, and others.

Suggested Citation

  • Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:531318
    DOI: 10.1155/S0161171286000935
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    Cited by:

    1. Budi Nurwahyu, 2019. "Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b -Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-14, December.
    2. Ghosh, S.K. & Nahak, C., 2020. "An extension of Lakzian-Rhoades results in the structure of ordered b-metric spaces via wt-distance with an application," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    3. Sharma, Sushil & Deshpande, Bhavana, 2009. "Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2242-2256.
    4. Rale M. Nikolić & Rajandra P. Pant & Vladimir T. Ristić & Aleksandar Šebeković, 2022. "Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    5. Erdal Karapınar & Ravi P. Agarwal & Seher Sultan Yeşilkaya & Chao Wang, 2022. "Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey," Mathematics, MDPI, vol. 10(17), pages 1-76, August.
    6. Muhammad Shoaib & Muhammad Sarwar, 2016. "Multivalued Fixed Point Theorems for Generalized Contractions and Their Applications," Journal of Mathematics, Hindawi, vol. 2016, pages 1-8, October.
    7. Zoran D. Mitrović & Hassen Aydi & Nawab Hussain & Aiman Mukheimer, 2019. "Reich, Jungck, and Berinde Common Fixed Point Results on ℱ-Metric Spaces and an Application," Mathematics, MDPI, vol. 7(5), pages 1-10, April.
    8. Deshpande, Bhavana, 2009. "Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2722-2728.
    9. Zoran D. Mitrović & Abasalt Bodaghi & Ahmad Aloqaily & Nabil Mlaiki & Reny George, 2023. "New Versions of Some Results on Fixed Points in b -Metric Spaces," Mathematics, MDPI, vol. 11(5), pages 1-9, February.
    10. E. Karapınar & D. K. Patel & M. Imdad & D. Gopal, 2013. "Some Nonunique Common Fixed Point Theorems in Symmetric Spaces through Property," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, February.
    11. Xiaolan Liu & Mi Zhou & Arslan Hojat Ansari & Naeem Saleem & Mukesh Kumar Jain, 2023. "Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application," Mathematics, MDPI, vol. 12(1), pages 1, December.
    12. Rqeeb Gubran & Mohammad Imdad, 2016. "Results on Coincidence and Common Fixed Points for (ψ,φ) g -Generalized Weakly Contractive Mappings in Ordered Metric Spaces," Mathematics, MDPI, vol. 4(4), pages 1-13, December.
    13. Piyachat Borisut & Poom Kumam & Vishal Gupta & Naveen Mani, 2019. "Generalized ( ψ , α , β )—Weak Contractions for Initial Value Problems," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    14. R. K. Bisht, 2012. "Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-12, July.
    15. Abd EL-Monsef, M.E. & Abu-Donia, H.M. & Abd-Rabou, Kh., 2009. "New types of common fixed point theorems in 2-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1435-1441.
    16. Mohammad Imdad & Sunny Chauhan, 2013. "Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems," International Journal of Analysis, Hindawi, vol. 2013, pages 1-10, May.
    17. P. Charoensawan & W. Atiponrat, 2017. "Common Fixed Point and Coupled Coincidence Point Theorems for Geraghty’s Type Contraction Mapping with Two Metrics Endowed with a Directed Graph," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, November.
    18. Pooja Dhawan & Jatinderdeep Kaur, 2019. "Some Common Fixed Point Theorems in Ordered Partial Metric Spaces via ℱ-Generalized Contractive Type Mappings," Mathematics, MDPI, vol. 7(2), pages 1-11, February.
    19. Cho, Yeol Je & Sedghi, Shaban & Shobe, Nabi, 2009. "Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2233-2244.
    20. Manoj Kumar & Pankaj Kumar & Sanjay Kumar, 2013. "Some Common Fixed Point Theorems in Generalized Metric Spaces," Journal of Mathematics, Hindawi, vol. 2013, pages 1-7, April.
    21. Abu-Donia, H.M., 2007. "Common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 538-543.
    22. Hemant Kumar Nashine & Hassen Aydi, 2012. "Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-23, July.
    23. Watchareepan Atiponrat & Pariwate Varnakovida & Pharunyou Chanthorn & Teeranush Suebcharoen & Phakdi Charoensawan, 2023. "Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations," Mathematics, MDPI, vol. 11(15), pages 1-20, August.
    24. J. R. Morales & E. M. Rojas, 2012. "Some Generalizations of Jungck's Fixed Point Theorem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-19, November.
    25. Nesrin Manav Tatar & Ravi P. Agarwal, 2023. "Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space," Mathematics, MDPI, vol. 11(21), pages 1-15, October.

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