Document Type: Research Paper
Authors
- G. Soleimani Rad ^{} ^{1}
- I. Altun ^{2}^{, 3}
^{1} Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
^{2} Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey
^{3} King Saud University, College of Science, Riyadh, Saudi Arabia
Abstract
In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize well-known comparable results in the literature.
Keywords
Main Subjects
[1] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416-420.
[2] M. Abbas, B.E. Rhoades and T. Nazir, Common fixed points for four maps in cone metric spaces, Appl. Math. Comput. 216 (2010), 80-86.
[3] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1999.
[4] I. Altun, Common fixed point theorems for weakly increasing mappings on ordered uniform spaces, Miskolc Math. Notes. 12 (1) (2011), 3-10.
[5] I. Altun and C. Cevik, Some common fixed point theroems in vector metric spaces, Filomat. 25 (1) (2011), 105-113.
[6] M. Arshad, A. Azam and P. Vetro, Some common fixed point results in cone metric spaces, Fixed Point Theory Appl. (2009), Article ID 493965.
[7] C. Cevik and I. Altun, Vector metric space and some properties, Topol. Met. Nonlin. Anal. 34 (2) (2009), 375-382.
[8] A.S. Cvetkovi´c, M.P. Stani´c, S. Dimitrijevi´c and S. Simi´c, Common fixed point theorems for four mappings on cone metric type space, Fixed Point Theory Appl. (2011), Article ID 589725.
[9] B. Fisher, Four mappings with a common fixed point, J. Univ. Kuwait Sci. 8 (1981), 131-139.
[10] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1467-1475.
[11] S. Jankovi´c, Z. Kadelburg and S. Radenovi´c, On cone metric spaces; a survey, Nonlinear Anal. 74 (2011), 2591-2601.
[12] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Am. Math. Soc. 103 (1988), 977-983.
[13] G. Jungck and B.E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory. (7) (2) (2006), 287-296.
[14] H. Rahimi, B.E. Rhoades, S. Radenovi´c and G. Soleimani Rad, Fixed and periodic point theorems for Tcontractions on cone metric spaces, Filomat. 27 (5) (2013), 881-888.
[15] H. Rahimi and G. Soleimani Rad, Common fixed point theorems and c-distance in ordered cone metric spaces, Ukrainian Mathematical Journal. 65 (12) (2014), 1845-1861.
[16] H. Rahimi, P. Vetro and G. Soleimani Rad, Some common fixed point results for weakly compatible mappings in cone metric type space, Miskolc Math. Notes. 14 (1) (2013), 233-243.
[17] S. Rezapour and R. Hamlbarani, Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008), 719-724.
[18] P.P. Zabreiko, K-metric and K-normed linear spaces: survey, Collect. Math. 48 (1997), 825-859.