International Journal of Nonlinear Analysis and Applications

Coincidence and common fixed points in metric space over Banach algebra

Document Type : Research Paper

Author

Guest Faculty, Doon University, Dehradun, Uttarakhand-248001, India

Abstract

The purpose of this paper is to obtain coincidence and common fixed point theorems for two pairs of weakly commuting self mappings in cone metric space over unital Banach algebra. Moreover, an example is given in the support of the main result and show that the result is more general than the results in present literature.

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] S.M. Abusalim and M.S.M. Noorani, Fixed point and common fixed point theorems on ordered cone b-metric spaces, Abstr. Appl. Anal. 2013 (2013), 7 pages.
[3] I. Altun and G. Durmaz, Some fixed point theorems on ordered cone metric spaces, Rend. Circ. Mate. Palermo 58 (2009), 319–325.
[4] W.S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010), 2559–2261.
[5] Y. Feng and W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory 11 (2010), 259–263.
[6] H. Hang and S. Randenovic, Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications, J. Nonlinear Sci. Appl. 8 (2015), 787–799.
[7] H. Huang and S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl. 2013 (2013), 10 pages.
[8] L.Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468–1476.
[9] S. Jankoric, Quasi-contraction on a cone metric space, Appl. Math Lett. 22 (2009), 728–731.
[10] S. Jannkovic, Z. Kaslburg and S. Radenovic, On the cone metric space, a survey, Nonlinear Anal. 74 (2011), 2591–2601.
[11] H. Liu and S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz maps, Fixed Point Theory Appl. 2013 (2013), 10 pages.
[12] S. Radenoviic and B.E. Rhoades, Fixed point theorem for two non-self maps in cone metric spaces, Comput. Math. Appl. 57 (2009), 1701–1707.
[13] W. Rudin, Functional analysis, McGraw-Hill, New York, 1991.
[14] S. Xu and S. Radenoviic, Fixed point theorems of generalized Lipschitz maps on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory Appl. 2014 (2014), 12 pages.
[15] Qi Yan, J. Yin and T. Wang, Fixed point and common fixed point theorems on ordered cone metric spaces over Banach algebras, J. Nonlinear Sci. Appli. 9 (2016), 1581–1589.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 479-484
  • Receive Date: 14 July 2020
  • Revise Date: 12 April 2021
  • Accept Date: 06 July 2021