Common fixed point theorem for weakly compatible mappings in Sm metric space

Authors

  • Mallaiah Katta N Government Polytechnic, Hyderabad, India
  • Srinivas Veladi University college of science OU, Hyderabad,India

DOI:

https://doi.org/10.23755/rm.v43i0.808

Keywords:

weakly compatible mappings, reciprocally continuous mappings and semi compatible mappings.

Abstract

In the present paper, at first, we study the structure of the newly Smmetric space, which is a union of S-metric space and multiplicative metric space with new contraction condition. We have proved a common fixed point theorem in Sm metric space by applying the concepts of the weakly compatible mappings, semi-compatible mappings, and reciprocally continuous mappings. This result generalizes and improves many common fixed point theorems in S-metric space and multiplicative metric space . Further, we also provide some examples to support our result.

References

A.E. Bashirov, E. Mısırlı Kurpınar, and A. Özyapıcı, "Multiplicative calculus and its applications," Journal of mathematical analysis and applications, vol. 337, no. 1, pp. 36-48, 2008.

A.N.A. Abdou, "Common fixed point results for compatible-type mappings in multiplicative metric spaces," J. Nonlinear Sci. Appl., vol. 9, pp. 2244-2257, 2016.

N.Y. Özgür and N. Taş, "Some generalizations of fixed-point theorems on s-metric spaces," in Essays in Mathematics and its Applications, Springer, pp. 229-261, 2016.

R.P. Agarwal, E. Karapınar, and B. Samet, "An essential remark on fixed point results on multiplicative metric spaces," Fixed point theory and applications, vol. 2016, no. 1, pp. 1-3, 2016.

S. Sedghi, N. Shobkolaei, M. Shahraki, and T. Došenović, "Common fixed point of four maps in s-metric spaces," Mathematical Sciences, vol. 12, no. 2, pp. 137-143, 2018.

S. Chaipornjareansri, "Fixed point theorems for generalized weakly contractive mappings in s-metric space," Thai Journal of Mathematics, pp. 50-62, 2018.

N.V. Dung, "On coupled common fixed points for mixed weakly monotone maps in partially ordered s-metric spaces," Fixed Point Theory and Applications, vol. 2013, no. 1, pp. 1-17, 2013.

R.P. Pant, "Common fixed points of four mappings," Bull. Cal. Math. Soc., vol. 90, pp. 281-286, 1998.

M.K. Jain and M.S. Khan, "Generalization of semi compatibility with some fixed point theorems under strict contractive condition," Applied Mathematics E-Notes, vol. 17, pp. 25-35, 2017.

K. Mallaiah and V. Srinivas, "Common fixed point of four maps in sm-metric space," International Journal of Analysis and Applications, vol. 19, no. 6, pp. 915-928, 2021.

M.A. Al-Thagafi and N. Shahzad, "Generalized i-nonexpansive self-maps and invariant approximations," Acta Mathematica Sinica, English Series, vol. 24, no. 5, pp. 867-876, 2008.

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Published

2023-06-30

Issue

Vol. 47 (2023)

Section

Volume 47-2023

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