10.30495/maca.2021.1944542.1037

Bicomplex valued bipolar metric spaces and fixed point theorems

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

Published in Issue 2022-01-01

How to Cite

Bicomplex valued bipolar metric spaces and fixed point theorems. (2022). Mathematical Analysis and Its Contemporary Applications, 4(1). https://doi.org/10.30495/maca.2021.1944542.1037

PDF views: 21

Abstract

The concept of bicomplex valued bipolar metric space is introduced in this article, and some properties are derived. Also, some fixed point results of contravariant maps satisfying rational inequalities are proved for bicomplex valued bipolar metric spaces.

Keywords

  • Bipolar metric space,
  • Bicomplex number,
  • Complex valued metric space,
  • Fixed point

References

  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. I. Beg, S. K. Datta and D. Pal, Fixed point in bicomplex valued metric spaces, Int. J. Nonlinear Anal. Appl., 12(2021), 717-727.
  3. 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), 115-126.
  4. S.K. Datta, D. Pal, R. Sarkar and A. Manna, On a common fixed point theorem in a bicomplex valued b-metric spaces, Montes Taurus J. Pure Appl. Math., 3(2021), 358-366.
  5. S.K. Datta, D. Pal, N. Biswas and R. Sarkar, On the study of common fixed point theorem in a bicomplex valued b-metric spaces, J. Cal. Math. Soc., 16(2020), 73-94.
  6. S.K. Datta, D. Pal, R. Sarkar and J. Saha, Some common fixed point theorems for contractive mappings in bicomplex valued b-metric spaces, Bull. Cal. Math. Soc., 112(2021), 329-354.
  7. I.H. Jebril, S.K. Datta,R. Sarkar and N. Biswas, Common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces, J. Interdisc. Math., 22(2019), 1071-1082.
  8. G. N. V. Kishore, K. P. R. Rao, H. Isik, B. S. Rao and A. Sombabu, Covariant mappings and coupled fixed point results in bipolar metric spaces, Int. J. Nonlinear Anal. Appl., 12(2021), 1-15.
  9. G. N. V. Kishore, R. P. Agarwal, B. S. Rao and R. V. N. S. Rao, Caristi type cyclic contrac-tion and common fixed point theorems in bipolar metric spaces with applications, Fixed Point Theory Appl., 21(2018), 1-13.
  10. C. G. Moorthy and G. Siva, Bipolar multiplicative metric spaces and fixed point theorems of covariant and contravariant mappings, Math. Anal. Convex Optim., 2(2021), 1-11.
  11. A. Mutlu and U. Gurdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl., 9 (2016), 5362-5373.
  12. A. Mutlu, K. Ozkan and U. Gurdal, Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl. Math., 10(2017), 655-667.
  13. D. Pal, R. Sarkar, A. Manna and S. K. Datta, A common fixed point theorem for six mappings in bicomplex valued metric spaces, J. Xi'an Univ. Architect. Technol. 13(2021), 168-176.
  14. C. Segre, Le rappresentazioni reali delle forme complesse a gli enti iperalgebrici, Math. Ann., 40(1892), 413-467.
  15. B. Srinuvasa Rao and G. N. V. Kishore, Common fixed point theorems in bipolar metric spaces with applications to integral equations, Int. J. Eng. Technol., 7(2018), 1022-1026.