Fixed points in tricomplex valued S-metric spaces with applications

Document Type : Research Paper

Author

Department of Mathematics, Alagappa University, Karaikudi-630 003, India

Abstract

The concept of tricomplex valued S-metric space is introduced in this article, and some properties are derived. Also, some fixed point results of contraction maps satisfying various types of rational inequalities are proved for tricomplex valued S-metric spaces. Moreover, an example is given to illustrate our main result. Furthermore, an existence theorem for the unique solution to the linear system of equations is obtained by using our main result.

Keywords

[1] A. Azam, B. Fisher, and M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 32 (2011), 243–253.
[2] J. Choi, S. K. Datta, T. Biswas, and N. Islam, Some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued metric spaces, Honam Math. J. 39 (2017), no. 1, 115–126.
[3] G. Mani, A.J. Gnanaprakasam, A.U. Haq, I.A. Baloch, and F. Jarad, Common fixed point theorems on tricomplex valued metric space, Math. Prob. Engin. 2022 (2022), 12 pages.
[4] N.M. Mlaika, Common fixed points in complex S-metric space, Adv. Fixed Point Theory 4 (2014), 509–524.
[5] N.Y. Ozgur and N. Tas, The Picard theorem on S-metric spaces, Acta Math. Sci. 38 (2018), 1245–1258.
[6] G.B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, New York, NY, USA, 1991.
[7] K. Prudhvi, Fixed point theorems in S-metric spaces, Univer. J. Comput. Math. 3 (2015), 19–21.
[8] S. Sedghi and N.V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik, 66 (2014), 113–124.
[9] S. Sedghi, N. Shobe, and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik 64 (2012), 258–266.
[10] C. Segre, Le rappresentazioni reali delle forme complesse a Gli Enti iperalgebrici, Math. Ann. 40 (1892), no. 3, 413–467.
[11] G. Siva, Fixed point theorems in tricomplex valued bipolar metric spaces, Roman. J. Math. Comput. Sci. 12 (2022), 4–74.
[12] G. Siva, Fixed points of contraction mappings with variations in S-metric space domains, Math. Student 91 (2022), 173–185.
[13] G. Siva, Fixed points in bicomplex valued S-metric spaces with applications, Surveys Math. Appl. 18 (2023), 329–341.
[14] G. Siva, and S. Loganathan, Weak convergence of fixed point iterations in S-metric spaces, J. Mahani Math. Res. 13 (2023), 565–576.
[15] G. Siva, Complex valued bipolar metric spaces and fixed point theorems., Commun. Nonlinear Anal. 11 (2023), no. 2, 1–10.
[16] G. Siva, Bicomplex valued bipolar metric spaces and fixed point theorems, Math. Anal. Contemp. Appl. 4 (2022), no. 1, 29–43.
Volume 16, Issue 3
March 2025
Pages 115-123
  • Receive Date: 13 August 2023
  • Revise Date: 23 January 2024
  • Accept Date: 03 February 2024