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.

Keywords: Fixed point; cone 2-metric; $J$-weakly compatible pair; $\alpha$-$\varphi$-contractive mapping; ternary relation.

MSC: 47H10, 54H25

Pages:  14$-$24     

Volume  73 ,  Issue  1 ,  2021