FIXED POINTS OF EXPANSIVE MAPS IN PARTIAL CONE METRIC SPACES

Year 2014, Volume: 27 Issue: 4, 1085 - 1091, 03.06.2014

Jerolina Fernandez , Kalpana Saxena Neeraj Malviya

Abstract

Matthews [10] introduced a new distance P on a nonempty set X, which he called a partial metric. Sonmez [16] introduced the notion of partial cone metric space and its topological characterization. In present paper, we define expansive map in partial cone metric space and prove some fixed point theorems for such maps. Our results extend the results of [4], [9], [17] in partial cone metric space. An example is given to support the usability of our results.

Keywords

Partial cone metric space, expanding mapping, fixed point.

References

• Abbas Mujahid , Rhoades B.E. ,Fixed and periodic point results in cone metric spaces, Applied Mathematics Letters , 22, 511-515, (2009).
• Cho S.H, Bae, J.S: Common fixed point theorems for mappings satisfying property (E.A) on cone metric space. Math.Comput.Model.53, 945-951, (2011).
• Haung L.-G. , Zhang X., Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal.Appl. 332,1368 -1376, (2007).
• Huang Xianjiu, Zhu Chuanxi, Wen Xi, Fixed point theorems for expanding mappings in partial metric spaces, An. St. Univ. Ovidius Constanta, Vol. 20(1), 213- 224,(2012).
• Jankovic, S, Kadelburg, Z, Radenovic, S: On cone metric spaces: a survey. Nonlinear Anal.4(7), 2591-2601, (2011).
• Jungck G., Commuting mappings and fixed points The American Mathematical Monthly, Vol.83,no.4, PP.261- 263, (1976).
• Lin S. D., A common Şxed point theorem in abstract spaces, Indian Journal of Pure and Applied Mathematics, vol. 18, no. 8, pp. 685–690, (1987).
• Machuca R., A coincidence theorem The American Mathematical Monthly, Vol.74, no.5, P. 569, (1967).
• Malviya N. and Chouhan P., Fixed Point Of Expansive Type Mapping In N-Cone Metric Space, Mathematical Theory and Modeling, Vol.3, No.7, (2013).
• Matthews S., Partial metric topology, in: Proc. 8th Summer
• Applications..Ann. New York Acad. Sci. 728, 183-197, (1994). General Topology and S.,Common fixed points
• under [13] Rezapour Sh. and Hamlbarani R., Some notes on the paper: “Cone metric spaces and Şxed point theorems of contractive mappings”,Journal of Mathematical Analysis and Applications, vol. 345, no. 2,pp. 719–724, (2008).
• Rhoades B.E., A comparison of various definitions of contractive mappings. Tran. Am. Math.Soc.226, 257-290, (1977).
• Rzepecki B., On Şxed point theorems of Maia type, Publications de l’Institut Mathematique, vol.2842, pp. 179–186, (1980).
• Sonmez, A., (14 Jan, 2011), Fixed point theorems in partial cone metric spaces, arXiv:1101.2741v1[math.GN]. [17] Wang S. Z., Li B. Y., Gao Z. M., Iseki K., Some fixed point theorems for expansion mappings, Math. Japonica.29 ,631-636, (1984).
• Zhang S., Fixed point theory and its applications, Chongqing press, Chongqing China, (1984).