New coincidence and common fixed point theorems

Authors

  • S.L. Singh
  • Apichai Hematulin Nakhonratchasima Rajabhat University
  • Rajendra Pant SRM University Modinagar

DOI:

https://doi.org/10.4995/agt.2009.1792

Keywords:

Coincidence point, Fixed point, Banach contraction, Quasi-contraction, Asymptotic regularity

Abstract

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.

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Author Biography

Apichai Hematulin, Nakhonratchasima Rajabhat University

Department of Mathematics

References

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 (1966), 571–575.

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. 3 (1984), 429–434.

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, no. 2 (1993), 159–164.

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 Appl. math. 15, no. 8 (1984), 849–854.

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), 247–256.

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

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How to Cite

[1]
S. Singh, A. Hematulin, and R. Pant, “New coincidence and common fixed point theorems”, Appl. Gen. Topol., vol. 10, no. 1, pp. 121–130, Apr. 2009.

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