Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

COINCIDENCE AND COMMON FIXED POINTS OF NONCOMPATIBLEMAPS

  • Beg, Ismat (Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences) ;
  • Abbas, Mujahid (Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences)
  • Received : 2010.06.25
  • Accepted : 2010.09.17
  • Published : 2011.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

Fixed point theorems for two hybrid pairs of single valued and multivalued noncompatible maps under strict contractive condition are proved, without appeal to continuity of any map involved therein and completeness of underlying space. These results extend, unify and improve the earlier comparable known results.

Keywords

References

  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. A. Azam and I. Beg, Coincidence point of compatible multivalued mappings, Demonstratio Mathematica, 29 (1996), 17-22.
  3. I. Beg and M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory and Appl., 2006(2006) Article ID 74503, pages 1-7.
  4. I. Beg and M. Abbas, Fixed point, approximate fixed point and Kantorovich-Rubinstein maximum principle in convex metric spaces, J. Appl. Math & Computing, 27(2008), 211- 226. https://doi.org/10.1007/s12190-008-0037-4
  5. I. Beg and A. Azam, Fixed points of asymptotically regular multivalued mappings, J. Austral Math. Soc., 53(A)(1992), 313-326.
  6. I. Beg and A. Azam, Common fixed points for commuting and compatible maps, Discussiones Mathematicae: Differential Inclusions, 16 (1996), 121-135.
  7. I. Beg and B.S. Thakar, General iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings, Fixed Point Theory, 9(2) (2008), 407-421.
  8. L. S. Dube, A theorem on common fixed points of multivalued mappings, Annal. Soc. Sci. Bruxells, 84(4)(1975), 463-468.
  9. O. Hadzic, Common fixed point theorem for single valued and multivalued mappings, Rev. of Research for Sci. Math. Series., 18(1988), 145-151.
  10. G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261-263. https://doi.org/10.2307/2318216
  11. G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Soc., 103(1988), 977-983. https://doi.org/10.1090/S0002-9939-1988-0947693-2
  12. G. Jungck, Common fixed points for noncontinuous nonself maps on a nonmetric space, Far East J. Math. Sci., 4(2) (1996), 199-212.
  13. G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238.
  14. T. Kamran, Coincidence and fixed points for hybrid strict contractions, J. Math. Anal. Appl., 299 (2004), 235-241. https://doi.org/10.1016/j.jmaa.2004.06.047
  15. H. Kaneko and S. Sessa, Fixed point theorems for compatible multivalued and single valued mappings, Int. J. Math. Math. Sci., 12 (1989), 257-267. https://doi.org/10.1155/S0161171289000293
  16. H. G. LI, S-coincidence and S¡common fixed point theorems for two pairs of set-valued noncompatible mappings in metric space, J. Nonlinear Sci. Appl. 3 (2010) No.1, 55-62. https://doi.org/10.22436/jnsa.003.01.07
  17. Y. Liu, J. Wu and Z. Li, Common fixed points of single valued and multivalued maps, Int. J. Math. Math. Sci., 19 (2005), 3045-3055.
  18. S. B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math., 30 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  19. R. P. Pant, Common fixed point of noncommuting mappings, J. Math. Anal. Appl., 188(1994), 436-440. https://doi.org/10.1006/jmaa.1994.1437
  20. B. E. Rhoades, On multivalued f-nonexpansive maps, Fixed Point Theory Appl., 2 (2001), 89-92.
  21. S. Sessa, On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. Soc., 32(1982), 149-153.
  22. N. Shahzad, Invariant approximation and R- subweakly commuting maps, J. Math. Anal. Appl., 257(2001), 39-45. https://doi.org/10.1006/jmaa.2000.7274
  23. S. L. Singh and A. Kumar, Common fixed point theorems for contractive maps, Mat. Bech., 58(2006), 85-90.