New coincidence and common fixed point theorems

• Singh, S.L. ; Hematulin, Apichai ^[1] ; Pant, Rajendra ^[2]
  1. [1] Nakhonratchasima Rajabhat University
  2. [2] SRM University Modinagar
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 1, 2009, págs. 121-130
• Idioma: inglés
• DOI: 10.4995/agt.2009.1792
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we obtain some extensions and a generalization of a remarkable fixed point theorem of Proinov. Indeed, we obtain some coincidence and fixed point theorems for asymptotically regular non-self and self-maps without requiring continuity and relaxing the completeness of the space. Some useful examples and discussions are also given.

• Referencias bibliográficas
  • D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464.
  • http://dx.doi.org/10.1090/S0002-9939-1969-0239559-9
  • F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72...
  • http://dx.doi.org/10.1090/S0002-9904-1966-11544-6
  • Y. J. Cho, P. P. Murthy and G. Jungck, A theorem of Meer-Keeler type revisited, Internat J. Math. Math. Sci. 23 (2000), 507–511.
  • http://dx.doi.org/10.1155/S0161171200002258
  • Lj. B. ´Ciri´c, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273.
  • http://dx.doi.org/10.2307/2040075
  • S. Itoh and W. Takahashi, Single valued mappings, mutivalued mappings and fixed point theorems, J. Math. Anal. Appl. 59 (1977), 514–521.
  • http://dx.doi.org/10.1016/0022-247X(77)90078-6
  • J. Jachymski, Equivalent conditions and the Meir-keeler type theorems, J. Math. Anal. Appl. 194 (1995), 293–303.
  • http://dx.doi.org/10.1006/jmaa.1995.1299
  • G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly. 83 (1976), 261–263.
  • http://dx.doi.org/10.2307/2318216
  • G. Jungck and B. E. Rhoades, Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math. 29, no. 3 (1988), 227–238.
  • K. H. Kim, S. M. Kang and Y. J. Cho, Common fixed point of −contractive mappings, East. Asian Math. J. 15 (1999), 211–222.
  • T. C. Lim, On characterization of Meir-Keeler contractive maps, Nonlinear Anal. 46 (2001), 113–120.
  • http://dx.doi.org/10.1016/S0362-546X(99)00448-4
  • J. Matkowski, Fixed point theorems for contractive mappings in metric spaces, Cas. Pest. Mat. 105 (1980), 341–344.
  • A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326–329.
  • http://dx.doi.org/10.1016/0022-247X(69)90031-6
  • S. A. Naimpally, S. L. Singh and J. H. M. Whitfield, Coincidence theorems for hybrid contractions, Math. Nachr. 127 (1986), 177–180.
  • http://dx.doi.org/10.1002/mana.19861270112
  • S. Park and B. E. Rhoades, Meir-Keeler type contractive conditions, Math. Japon. 26 (1981), 13–20.
  • P. D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. 64 (2006), 546– 557.
  • http://dx.doi.org/10.1016/j.na.2005.04.044
  • R. P. Pant, Common fixed points of noncommuting mappings J. Math. Anal. Appl. 188 (1994), 436–440.
  • http://dx.doi.org/10.1006/jmaa.1994.1437
  • B. E. Rhoades, A comparison of various definitions of contracting mappings, Trans. Amer. Math. Soc. 226 (1977), 257–290.
  • http://dx.doi.org/10.1090/S0002-9947-1977-0433430-4
  • B. E. Rhoades, S. L. Singh and Chitra Kulshrestha, Coincidence theorems for some multivalued mappings, Internat. J. Math. Math. Sci. 7, no....
  • http://dx.doi.org/10.1155/S0161171284000466
  • S. Romaguera, Fixed point theorems for mappings in complete quasi-metric spaces, An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si Sect¸. I a Mat. 39,...
  • K. P. R. Sastry, S. V. R. Naidu, I. H. N. Rao and K. P. R. Rao, Common fixed point points for asymptotically regular mappings, Indian J. Pure...
  • S. L. Singh, K. Ha and Y. J. Cho, Coincidence and fixed point of nonlinear hybrid contractions, Internat. J. Math. Math. Sci. 12, no. 2 (1989),...
  • http://dx.doi.org/10.1155/S0161171289000281
  • S. L. Singh and S. N.Mishra, Coincidence and fixed points of nonself hybrid contractions, J. Math. Anal. Appl. 256 (2001), 486–497.
  • http://dx.doi.org/10.1006/jmaa.2000.7301