The Chatterjea fixed point theorem on CCRM - spaces

K. Prudhvi

doi:10.5281/zenodo.18607793

The Chatterjea fixed point theorem on CCRM - spaces

K. Prudhvi

Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Telangana, India.

Received: 17 Sep 2025 | Accepted: 02 Dec 2025 | Final Version: 31 Dec 2025

Abstract

In the present paper, we obtain a fixed point result on CCRM (Complete Cone Rectangular) - Spaces. We extend the results of Jleli and samet results existing in the literature.

Keywords:

Cone metric space, cone rectangular metric space, fixed point, normal cone.

1. Introduction

Banach fixed point theorem is first and foremost one in fixed point theory and lot of generalizations has been done in this theorem. Huang and Zhang[5] have introduced the concept of cone metric space, where the set of real numbers is replaced by an ordered Banach space and they obtained fixed point results for contractive type conditions in normal cone metric space. Subsequently many authors has been studying and generalizing this cone metric space...

References

A. Azam, M. Arshad and I. Beg, Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3 (2009), 236–241.
A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, The Journal of Nonlinear Sciences, 1 (2008), no. 1, 45–48.
A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces, Publicationes Mathematicae Debrecen, 57 (1–2) (2000), 31–37.
M. Jleli and B. Samet, The Kannan’s fixed point theorem in a cone rectangular metric space, Nonlinear Sciences and Applications, 2 (2009), no. 3, 161–167.
L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332 (2) (2007), 1468–1476.
R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society, 60 (1968), 71–76.
S. Moradi, Kannan fixed point theorem on complete metric spaces and on generalized metric spaces depended on another function, arXiv:0903.1577v1 [math.FA], 9 March 2009, 1–6.
K. Prudhvi, Study on “Fixed Point Results” for pair of maps in CMS, Asian Basic and Applied Research Journal, 5 (1) (2023), 129–131.
K. Prudhvi, A unique common fixed point theorem in cone metric spaces, Advances in Fixed Point Theory, 3 (2013), no. 1, 70–76.
K. Prudhvi, Study on fixed points for OWC in symmetric spaces, Asia Mathematika, 7 (3) (2023), 72–75.
K. Prudhvi, Common fixed points on occasionally weakly compatible self-mappings in CMS, Asia Mathematika, 7 (2) (2023), 13–16.
K. Prudhvi, Results on fixed points for WC-mappings satisfying generalized contractive condition in C-metric spaces, Asia Mathematika, 8 (1) (2024), 112–117.
K. Prudhvi, A unique common fixed point result for compatible reciprocal continuous four self-maps in complete metric space, Asia Mathematika, 8 (3) (2024), 10–13.
K. Prudhvi, Study on extended B-K fixed point theorem on CGM-space depended on another function, Asia Mathematika, 5 (2) (2025), 25–28.
K. Prudhvi, A unique fixed point result on C-G-MS, Asia Mathematika, 9 (2) (2025), 47–50.
B. E. Rhoades, A comparison of various definitions of contractive mappings, Transactions of the American Mathematical Society, 226 (1977), 257–290.

[ref1] A. Azam, M. Arshad and I. Beg, Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3 (2009), 236–241.

[ref2] A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, The Journal of Nonlinear Sciences, 1 (2008), no. 1, 45–48.

[ref3] A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces, Publicationes Mathematicae Debrecen, 57 (1–2) (2000), 31–37.

[ref4] M. Jleli and B. Samet, The Kannan’s fixed point theorem in a cone rectangular metric space, Nonlinear Sciences and Applications, 2 (2009), no. 3, 161–167.

[ref5] L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332 (2) (2007), 1468–1476.

[ref6] R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society, 60 (1968), 71–76.

[ref7] S. Moradi, Kannan fixed point theorem on complete metric spaces and on generalized metric spaces depended on another function, arXiv:0903.1577v1 [math.FA], 9 March 2009, 1–6.

[ref8] K. Prudhvi, Study on “Fixed Point Results” for pair of maps in CMS, Asian Basic and Applied Research Journal, 5 (1) (2023), 129–131.

[ref9] K. Prudhvi, A unique common fixed point theorem in cone metric spaces, Advances in Fixed Point Theory, 3 (2013), no. 1, 70–76.

[ref10] K. Prudhvi, Study on fixed points for OWC in symmetric spaces, Asia Mathematika, 7 (3) (2023), 72–75.

[ref11] K. Prudhvi, Common fixed points on occasionally weakly compatible self-mappings in CMS, Asia Mathematika, 7 (2) (2023), 13–16.

[ref12] K. Prudhvi, Results on fixed points for WC-mappings satisfying generalized contractive condition in C-metric spaces, Asia Mathematika, 8 (1) (2024), 112–117.

[ref13] K. Prudhvi, A unique common fixed point result for compatible reciprocal continuous four self-maps in complete metric space, Asia Mathematika, 8 (3) (2024), 10–13.

[ref14] K. Prudhvi, Study on extended B-K fixed point theorem on CGM-space depended on another function, Asia Mathematika, 5 (2) (2025), 25–28.

[ref15] K. Prudhvi, A unique fixed point result on C-G-MS, Asia Mathematika, 9 (2) (2025), 47–50.

[ref16] B. E. Rhoades, A comparison of various definitions of contractive mappings, Transactions of the American Mathematical Society, 226 (1977), 257–290.