Some Results in Cone Metric Space, Using Semi-Compatible and Reciprocally Continuous Mappings

Authors

DOI:

https://doi.org/10.26713/cma.v13i5.2253

Keywords:

Common fixed point, Coincidence point, Cone metric space, Semi-compatible, Reciprocally continuous and sub sequentially continuous mappings

Abstract

In this paper, we establish a result in cone metric space by generalizing the theorem proved by Jain et al. (Compatibility and weak compatibility for four self maps in a cone metric space, Bulletin of Mathematical Analysis and Applications 2(1) (2010), 15 – 24) by employing certain weaker conditions such as semi-compatible, reciprocally continuous and sub sequentially continuous mappings. Further, our result is supported by discussing a relevant example.

Downloads

References

M. Abbas and B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Applied Mathematics Letters 22(4) (2009), 511 – 515, DOI: 10.1016/j.aml.2008.07.001.

M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications 341(1) (2008), 416 – 420, DOI: 10.1016/j.jmaa.2007.09.070.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3(1) (1922), 133 – 181, URL: https://eudml.org/doc/213289.

O. P. Chauhan, N. Singh, D. Singh and L. N. Mishra, Common fixed point theorems in cone metric spaces under general contractive conditions, Scientific Publications of the State University of Novi Pazar - Series A 9(2) (2017), 133 – 149, URL: https://web.archive.org/web/20180722210103id_/http://scindeks-clanci.ceon.rs/data/pdf/2217-5539/2017/2217-55391702133C.pdf.

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, DOI: 10.1016/j.jmaa.2005.03.087.

D. Ilic and V. Rako ´ cevi ˇ c, Quasi-contraction on a cone metric space, Applied Mathematics Letters 22(5) (2009), 1674 – 1679, DOI: 10.1016/j.aml.2008.08.011.

S. Jain, S. Jain and L. Bahadur, Compatibility and weak compatibility for four self maps in a cone metric space, Bulletin of Mathematical Analysis and Applications 2(1) (2010), 15 – 24, URL: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/BMAA/repository/docs/BMAA2-1-3.pdf.

P. Malviya, V. Gupta and V. H. Badshah, Common fixed point theorem for semi compatible pairs of reciprocal continuous maps in Menger spaces, Annals of Pure and Applied Mathematics 11(2) (2016), 139 – 144, URL: http://researchmathsci.org/apamart/APAM-V11n2-19.pdf.

Sh. Rezapour and R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, Journal of Mathematical Analysis and Applications 345(2) (2008), 719 – 724, DOI: 10.1016/j.jmaa.2008.04.049.

K. Satyanna and V. Srinvas, Fixed point theorem using semi compatible and sub sequentially continuous mappings in Menger space, Journal of Mathematical and Computational Science 10(6) (2020), 2503 – 2515, DOI: 10.28919/jmcs/4953.

G. Song, X. Sun, Y. Zhao and G. Wang, New common fixed point theorems for maps on cone metric spaces, Applied Mathematics Letters 23(9) (2010), 1033 – 1037, DOI: 10.1016/j.aml.2010.04.032.

V. Srinivas and B. V. Reddy, A common fixed point theorem on fuzzy metric space using weakly compatible and semi-compatible mappings, International Journal of Mathematics and Statistics Invention 4(9) (2016), 27 – 31, URL: https://ijmsi.org/Papers/Volume.4.Issue.9/E0409027031.pdf.

P. Vetro, Common fixed points in cone metric spaces, Rendiconti del Circolo Matematico di Palermo 56 (2007), 464 – 468, DOI: 10.1007/BF03032097.

Downloads

Published

30-12-2022
CITATION

How to Cite

Perala, C., & Srinivas, . V. (2022). Some Results in Cone Metric Space, Using Semi-Compatible and Reciprocally Continuous Mappings. Communications in Mathematics and Applications, 13(5), 1413–1426. https://doi.org/10.26713/cma.v13i5.2253

Issue

Vol. 13 No. 5 (2022)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.