New coincidence and common fixed point theorems

S.L. Singh, Apichai Hematulin, Rajendra Pant

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.


Keywords

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

Full Text:

PDF

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

Abstract Views

1126
Metrics Loading ...

Metrics powered by PLOS ALM


 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Fixed point theorems in Boolean vector spaces
D.P.R.V. Subba Rao, Rajendra Pant
Nonlinear Analysis: Theory, Methods & Applications  vol: 74  issue: 16  first page: 5383  year: 2011  
doi: 10.1016/j.na.2011.05.021



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt