Common fixed point theorems for generalized ordered contractive mappings on cone b--metric spaces over Banach algebras

Volume 9, Issue 11, pp 5766--5771
• 931 Views

Authors

Chuanzhi Bai - Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, P. R. China.

Abstract

In this paper, we introduce the concept of generalized ordered contractive mappings on cone b-metric spaces over Banach algebras and establish a new common some fixed point theorems of such mappings under some natural conditions. The results extend and improve recent related results.

Keywords

• Cone b-metric spaces over Banach algebras
• common fixed point
• ordered contractive mappings.

•  54H25
•  47H10

References

• [1] M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl., 2013 (2013), 25 pages

• [2] I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, 30 (1989), 26--37

• [3] L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468--1476

• [4] H. Liu, S. Y. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory and Appl., 2013 (2013), 10 pages

• [5] S. Radenović, B. E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl., 57 (2009), 1701--1707

• [6] W. Rudin, Functional analysis, Second edition, International Series in Pure and Applied Mathematics, McGraw- Hill, Inc., New York (1991)

• [7] M. H. Shah, N. Hussain, Nonlinear contractions in partially ordered quasi b-metric spaces, Commun. Korean Math. Soc., 27 (2012), 117--128

• [8] S. Y. Xu, S. Radenović, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory and Appl., 2014 (2014), 12 pages

• [9] J. D. Yin, T. Wang, Q. Yan, Fixed point theorems of ordered contractive mappings on cone metric spaces over Banach algebras, Fixed Point Theory and Appl., 2015 (2015), 13 pages

• [10] C. X. Zhu, C. F. Chen, X. Z. Zhang, Some results in quasi-b-metric-like spaces, J. Inequal. Appl., 2014 (2014), 8 pages