Weakly Compatible Maps and Fixed Points

Document Type : Original Scientific Paper

Authors

1 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran

10.22052/mir.2021.240433.1267

Abstract

Here, the existence of fixed points for weakly compatible maps is studied. The results are new generalization of the results of [5]. Finally, we study the new common fixed point theorems.

Keywords


[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] N. Cakić, Z. Kadelburg, S. Radenović and A. Razani, Common fixed point results in cone metric spaces for a family of weakly compatible maps, Adv. Appl. Math. Sci. 1 (2009) 183 − 207.
[3] L. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974) 267 − 237.
[4] M. Das and K. V. Naik, Common fixed point theorems for commuting maps on a metric space, Proc. Amer. Math. Soc. 77 (3) (1979) 369 − 373.
[5] L. -G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468 − 1476.
[6] D. Ilić and V. Rakoˇ cević, Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008) 876 − 882.
[7] G. Jungck, Commuting mappings and fixed point, Amer. Math. Monthly 83 (1976) 261 − 263.
[8] G. Jungck, Compatible mappings and common fixed point, Internat. J. Math. Math. Sci. 9 (1986) 771 − 779.
[9] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998) 227 − 238.
[10] F. Khojasteh, Z. Goodarzi and A. Razani, Some fixed point theorems of integral type contraction in cone metric spaces, Fixed Point Theory Appl. 2010 (2010) 189684.
[11] F. Khojasteh, A. Razani and S. Moradi, A Fixed point of generalized TF−contraction mappings in cone metric spaces, Fixed Point Theory Appl. 2011 (2011) 14.
[12] A. Razani, Results in Fixed Point Theory, Andisheh Zarin Publisher, Qazvin, 2010.
[13] A. Razani, V. Rakočević and Z. Goodarzi, Generalized ϕ-contraction for a pair of mappings on cone metric spaces, Appl. Math. Comput. 217 (22) (2011) 8899 − 8906.