Nonlinear Functional Analysis and Applications

  • 제26권5호
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  • Pages.1059-1075
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  • 2021
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  • 1229-1595(pISSN)
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  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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REMARKS ON CERTAIN NOTED COINCIDENCE THEOREMS: A UNIFYING AND ENRICHING APPROACH

  • Alam, Aftab (Department of Mathematics Aligarh Muslim University) ;
  • Hasan, Mohd. (Department of Mathematics Jazan University) ;
  • Imdad, Mohammad (Department of Mathematics Aligarh Muslim University)
  • 투고 : 2020.09.13
  • 심사 : 2021.04.12
  • 발행 : 2021.12.15
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초록

In this paper, we unify and enrich the well-known classical metrical coincidence theorems on a complete metric space due to Machuca, Goebel and Jungck. We further extend our newly proved results on a subspace Y of metric space X, wherein X need not be complete. Finally, we slightly modify the existing results involving (E.A)-property and (CLRg)-property and apply these results to deduce our coincidence and common fixed point theorems.

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과제정보

All the authors are grateful to a learned referee for his/her critical readings and pertinent comments on the earlier version of the manuscript.

참고문헌

  1. M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188. https://doi.org/10.1016/S0022-247X(02)00059-8
  2. R.P. Agarwal, R.K. Bisht and N. Shahzad, Comparison of various noncommuting conditions in metric fixed point theory and their applications, Fixed Point Theory Appl., 2014, 2014:38, 33 pp.
  3. G. Baxter, On fixed points of the composite of commuting functions, Proc. Amer. Math. Soc., 15 (1964), 851-856. https://doi.org/10.1090/S0002-9939-1964-0184217-8
  4. W.M. Boyce, Commuting functions with no common fixed point, Abstract 67T-218, Notices Amer. Math. Soc., 14 (1967), 280.
  5. W.M. Boyce, Commuting functions with no common fixed point, Trans. Amer. Math. Soc., 137 (1969), 77-92. https://doi.org/10.2307/1994788
  6. K. Goebel, A coincidence theorem, Bull. Acad. Pol. Sci. S'er. Sci. Math. Astron. Phys., 16 (1968), 733-735.
  7. J.P. Huneke, Two counter examples to a conjecture on commuting continuous functions of the closed unit interval, Abstract 67T-231, Notices Amer. Math. Soc., 14 (1967), 284.
  8. J P. Huneke, On common fixed points of commuting continuous functions on an interval, Trans. Amer. Math. Soc., 139 (1969), 371-381. https://doi.org/10.2307/1995330
  9. M. Imdad and J. Ali, Jungck's common fixed point theorem and E.A property, Acta Math. Sin., (Engl. Ser.) 24(1) (2008), 87-94. https://doi.org/10.1007/s10114-007-0990-0
  10. M. Imdad, J. Ali and L. Khan, Coincidence and fixed points in symmetric spaces under strict contractions, J. Math. Anal. Appl., 320(1) (2006), 352-360. https://doi.org/10.1016/j.jmaa.2005.07.004
  11. J.R. Isbell, Commuting mappings of trees, Research Problem #7, Bull. Amer. Math. Soc., 63 (1957), 419. https://doi.org/10.1090/S0002-9904-1957-10150-5
  12. G. Jungck, Commuting maps and fixed points, Amer. Math. Monthly, 83(4) (1976), 261-263. https://doi.org/10.2307/2318216
  13. G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (4) (1986), 771-779. https://doi.org/10.1155/S0161171286000935
  14. G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci., 4 (1996), 199-215.
  15. Z. Kadelburg, S. Radenovi'c and N. Shahzad, A note on various classes of compatible-type pairs of mappings and common fixed point theorems, Abstr. Appl. Anal., 2013, 2013:697151, 6 pp.
  16. R. Machuca, A coincidence theorem, Amer. Math. Monthly, 74 (1967), 569-572. https://doi.org/10.2307/2314896
  17. P.P. Murthy, Important tools and possible applications of metric fixed point theory, Proceedings of the Third World Congress of Nonlinear Analysts, Part 5 (Catania, 2000), Nonlinear Anal. TMA., 47(5) (2001), 3479-3490.
  18. R.P. Pant, Common fixed points of Lipschitz type mapping pairs, J. Math. Anal. Appl., 240 (1999), 280-283. https://doi.org/10.1006/jmaa.1999.6559
  19. K.P.R. Sastry and I.S.R. Krishna Murthy, Common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl., 250(2) (2000), 731-734. https://doi.org/10.1006/jmaa.2000.7082
  20. S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. Soc., 32 (1982), 149-153.
  21. W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011, 2011:637958, 14 pp.