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, α-φ-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-φ-contractions with respect to T are introduced. Some common fixed point results for g-contractions and g-φ-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