GENERALIZED CONTRACTIONS AND COMMON FIXED POINT THEOREMS CONCERNING DISTANCE


Authors

A. BAGHERI VAKILABAD - Dept. of Math., Islamic Azad University,Science and Research Branch, Tehran, Iran
S. MANSOUR VAEZPOUR - Dept. of Math., Amirkabir University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran


Abstract

In this paper we consider the generalized distance, present a generalization of Ćirić's generalized contraction fixed point theorems on a complete metric space and investigate a common fixed point theorem about a sequence of mappings concerning generalized distance.


Keywords


References

[1] M. Alimohammadi and M. Ramzanzadeh, On \(\Phi\)-Fixed point for maps on uniform spaces, J. of Nonlinear Science and Applications, 1(4)(2008), 241-243.
[2] A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, J. of Nonlinear Science and Applications, 1(1)(2008), 45-48.
[3] O. Kada, T. Suzuki and W. Takahashi, Nonconvex Minimization theorems and fixed point theorems in complete metric spaces, Math. Japon, 44 (1996), 381-391.
[4] D. Mihet, On Kannan fixed point principle in generalized metric spaces, J. of Nonlinear Science and Applications, 2(2)(2009), 92-96.
[5] I. R. Sarma, J. M. Rao2, and S. S. Rao, Contractions over generalized metric spaces, J. of Nonlinear Science and Applications, 2(3)(2009), 180-182.
[6] N. Shioji, T. Suzuki and W. Takahashi, Contractive mappings, Kannan mappings and metric completness, Proc. Amer. Math. Soc, 126 (1998), 3117-3124.
[7] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl, 253(2) (2001), 440-458.
[8] T. Suzuki, On Downing-Kirk's theorem, J. Math. Anal. Appl, 286 (2003), 453-458.
[9] T. Suzuki, Several fixed point theorems concerning \(\tau\)-distance, Fixed Point Theory and Applications, 3 (2004), 195-209.
[10] T. Suzuki, Generalized Caristi's fixed point theorems by Bae and othrs, J. Math. Anal. Appl, 302 (2005), 502-508.
[11] T. Suzuki, Thestrong Ekeland vriational principle, J. Math. Anal. Appl, 320 (2006), 787-794.
[12] W. Takahashi, Existence theorems generalazing fixed point theorems for multivalued mappings, ''Fixed Point Theory and Applications'' , 252(1991), 397-406.
[13] D. Tataru, Viscosity soluation of Hamilton-Jacbi equations with unbounded nonlinear terms, J. Math. Anal. Appl, 163 (1992), 345-392.
[14] L. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd)(N.S.), 12(26) (1971), 19-26.
[15] L. B. Ćirić, On a family of contractive maps and fixed-points, Publ. Inst. Math. (Beograd)(N.S.), 17(31) (1974), 45-51.
[16] L. B. Ćirić, A generalization of Banbch's contractions principle, Proc. Amer. Math. Soc, 45 (1974), 267-273.