New fixed and periodic point results on cone metric spaces

محورهای موضوعی : History and biography

Gh. Soleimani Rad ¹

1 - Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 13185-768, Iran

تاریخ دریافت : 1390/10/11 تاریخ پذیرش : 1390/10/11 تاریخ انتشار : 1390/12/11

کلید واژه: fixed point, Cone metric space, Property P, Property Q, Normal cone,

چکیده مقاله :

In this paper, several fixed point theorems for T-contraction of two maps on conemetric spaces under normality condition are proved. Obtained results extend and generalizewell-known comparable results in the literature.

منابع و مأخذ:

[1] M. Abbas, G. Jungck, Common xed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), pp. 416-420.

[2] M. Abbas, B.E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (2009), pp. 511-515.

[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. J. 3 (1922), pp. 133-181.

[4] L. B. Ciric , A generalization of Banach contraction principle, Proc. Amer. Math. Soc. 45 (1974), pp. 267-273.

[5] M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings", Math. Comput. Modelling. 54 (2011), pp. 1467-1472.

[6] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.

[7] G.E. Hardy, T.D. Rogers, A generalization of a xed point theorem of Reich, Canad. Math. Bull. 1 (6) (1973), pp. 201-206.

[8] L.G. Huang, X. Zhang, Cone metric spaces and xed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), pp. 1467-1475.

[9] G.S. Jeong, B.E. Rhoades, Maps for which F(T) = F(Tn), Fixed Point Theory Appl. 6 (2005), pp. 87-131.

[10] G. Jungck, Commuting maps and xed points, Amer. Math. Monthly 83 (1976), pp. 261-263.

[11] R. Kannan, Some results on xed points, Bull. Calcutta Math. Soc. 60 (1968), pp. 71-76.

[12] J.R. Morales, E. Rojas, Cone metric spaces and xed point theorems of T-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010), pp. 175-184.

[13] H. Rahimi, Gh. Soleimani Rad, Some xed point results in metric type space, J. Basic Appl. Sci. Res. 2 (9) (2012), pp. 9301-9308.

[14] S. Rezapour, R. Hamlbarani, Some note on the paper cone metric spaces and xed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008), pp. 719-724.

[15] B.E. Rhoades, A comparison of various denition of contractive mappings, Trans. Amer. Math. Soc.

266 (1977), pp. 257-290.

[16] G. Song, X. Sun, Y. Zhao, G. Wang, New common xed point theorems for maps on cone metric spaces, Appl. Math. Lett. 23 (2010), pp. 1033-1037.

[17] S. Wang, B. Guo, Distance in cone metric spaces and common xed point theorems, Appl. Math. Lett. 24 (2011), pp. 1735-1739.