대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권3호
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  • Pages.513-522
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  • 2012
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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FIXED POINTS OF OCCASIONALLY WEAKLY COMPATIBLE MAPPINGS USING IMPLICIT RELATION

  • 투고 : 2011.02.20
  • 발행 : 2012.07.31
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초록

In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.

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참고문헌

  1. C. T. Aage and J. N. Salunke, On fixed point theorems in fuzzy metric spaces, Int. J. Open Probl. Comput. Sci. Math. 3 (2010), no. 2, 123-131.
  2. M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), Article ID 54101, 9 pages.
  3. M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces, Panamer. Math. J. 18 (2008), no. 1, 55-62.
  4. M. Abbas and B. E. Rhoades, Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition, Math. Commun. 13 (2008), no. 2, 295-301.
  5. A. Aliouche and V. Popa, Common fixed point theorems for occasionally weakly com- patible mappings via implicit relations, Filomat 22 (2008), no. 2, 99-107. https://doi.org/10.2298/FIL0802099A
  6. A. Aliouche and V. Popa, General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math. 39 (2009), no. 1, 89-109.
  7. M. A. Al-Thagafi and N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica 24 (2008), no. 5, 867-876. https://doi.org/10.1007/s10114-007-5598-x
  8. M. A. Al-Thagafi and N. Shahzad, A note on occasionally weakly compatible maps, Int. J. Math. Anal. (Ruse) 3 (2009), no. 1-4, 55-58.
  9. I. Altun and D. Turkoglu, Some fixed point theorems on fuzzy metric spaces with implicit relations, Commun. Korean Math. Soc. 23 (2008), no. 1, 111-124. https://doi.org/10.4134/CKMS.2008.23.1.111
  10. A. Bhatt, H. Chandra, and D. R. Sahu, Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010), no. 1, 176-182. https://doi.org/10.1016/j.na.2010.03.011
  11. H. Bouhadjera, A general common fixed point theorem for occasionally weakly compatible maps, An. Univ. Oradea, Fasc. Mat. 17 (2010), no. 2, 17-22.
  12. H. Bouhadjera and A. Djoudi, Common fixed point theorems of Gregus type for occasionally weakly compatible maps satisfying contractive conditions of integral type, An. Univ. Oradea Fasc. Mat. 16 (2009), 145-152.
  13. H. Bouhadjera, A. Djoudi, and B. Fisher, A unique common fixed point theorem for occasionally weakly compatible maps, Surv. Math. Appl. 3 (2008), 177-182.
  14. H. Bouhadjera, A. Djoudi, and B. Fisher, A unique common fixed point theorem for occasionally weakly compatible maps, Bull. Allahabad Math. Soc. 24 (2009), no. 1, 1-6.
  15. H. Bouhadjera and C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible single and set-valued maps, HAL-00273238, Version 1, 15 April 2008.
  16. H. Bouhadjera and C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible maps, arXiv: 0812.3734v2 [math. FA], 17 June 2009.
  17. H. Chandra and A. Bhatt, Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, Int. J. Math. Anal. (Ruse) 3 (2009), no. 9-12, 563-570.
  18. S. S. Chang, Y. J. Cho, and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York, 2001.
  19. S. Chauhan, S. Kumar, and B. D. Pant, Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces, J. Adv. Research Pure Math. 3 (2011), no. 4, 17-23.
  20. S. Chauhan and B. D. Pant, Common fixed point theorems for occasionally weakly compatible mappings using implicit relation, J. Indian Math. Soc. 77 (2010), no. (1-4), 13-21.
  21. Lj. Ciric, B. Samet, and C. Vetro, Common fixed point theorems for families of occasionally weakly compatible mappings, Math. Comp. Model. 53 (2011), 631-636. https://doi.org/10.1016/j.mcm.2010.09.015
  22. O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Dordrecht: Kluwer Academic publishers, 2001.
  23. M. Imdad, S. Kumar, and M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations, Rad. Math. 11 (2002), no. 1, 135-143.
  24. G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.
  25. G. Jungck and B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7 (2006), no. 2, 287-296.
  26. G. Jungck and B. E. Rhoades, Erratum: "Fixed point theorems for occasionally weakly compatible mappings" [Fixed Point Theory 7 (2006), no. 2, 287-296; MR2284600], Fixed Point Theory 9 (2008), no. 1, 383-384.
  27. M. A. Khan and Sumitra, Common fixed point theorems for occasionally weakly compatible maps in fuzzy metric spaces, Far East J. Math. Sci. 41 (2010), no. 2, 285-293.
  28. K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535-537. https://doi.org/10.1073/pnas.28.12.535
  29. S. N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36 (1991), no. 2, 283-289.
  30. B. D. Pant and S. Chauhan, Common fixed point theorem for occasionally weakly com- patible mappings in Menger space, Surv. Math. Appl. 6 (2011), 1-7.
  31. V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157-163.
  32. V. Popa, A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33 (2000), no. 1, 159-164.
  33. V. Popa and D. Turkoglu, Some fixed point theorems for hybrid contractions satisfying an implicit relation, Stud. Cercet. Stint. Ser. Math. Univ. Bacau 1998 (1998), no. 8, 75-86.
  34. K. P. R. Sastry, G. A. Naidu, P. V. S. Prasad, V. M. Latha, and S. S. A. Sastry, A critical look at fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric spaces, Int. J. Math. Anal. (Ruse) 4 (2010), no. 27, 1341-1348.
  35. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. https://doi.org/10.2140/pjm.1960.10.313
  36. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier, North Holland, New York, 1983.
  37. V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on prob- abilistic metric spaces, Math. Systems Theory 6 (1972), 97-102. https://doi.org/10.1007/BF01706080
  38. S. Sharma and B. Deshpande, On compatible mappings satisfying an implicit relation in common fixed point consideration, Tamkang J. Math. 33 (2002), no. 3, 245-252.
  39. B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2005), no. 2, 439-448. https://doi.org/10.1016/j.jmaa.2004.07.036
  40. C. Vetro, Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces, Int. J. Mod. Math. 4 (2009), no. 3, 277-284.

피인용 문헌

  1. FIXED POINT THEOREMS IN MENGER SPACES USING AN IMPLICIT RELATION vol.35, pp.4, 2013, https://doi.org/10.5831/HMJ.2013.35.4.551