SOME COMMON FIXED POINT THEOREMS FOR CONTRACTIVE MAPPINGS IN CONE 2-METRIC SPACES EQUIPPED WITH A TERNARY RELATION

Authors

  • V. H. Badshah School of Studies in Mathematics, Vikram University, Ujjain, (M.P.), India Author
  • P. Bhagat Department of Applied Mathematics, NMIMS, Shirpur, India Author
  • S. Shukla Department of Applied Mathematics, Shri Vaishnav Institute of Technology and Science, Gram Baroli, Sanwer Road, Indore, 453331, (M.P.) India Author

Keywords:

Fixed point, cone 2-metric, $J$-weakly compatible pair, $\alpha$-$\varphi$-contractive mapping, ternary relation

Subjects:

47H10, 54H25

Abstract

In this paper, we study some common fixed point results in cone 2-metric spaces equipped with a ternary relation ${T}$. A weaker version of weakly compatible mappings, the notions of $g$-contractions with respect to ${T}$ and $g$-$\varphi$-contractions with respect to ${T}$ are introduced. Some common fixed point results for $g$-contractions and $g$-$\varphi$-contractions with respect to an arbitrary ternary relation ${T}$ and a transitive ternary relation respectively, are proved. To justify the newly introduced notions and results several examples are provided.

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Published

2021-01-15

Issue

Vol. 73 No. 1 (2021): Vol. 73, Issue 1

Section

Articles

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