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Some multidimensional fixed point theorems on partially preordered \(G^\ast\)-metric spaces under (\(\psi\),\(\phi\))-contractivity conditions. (English) Zbl 1293.54035

Summary: In this paper, we present some (unidimensional as well as) multidimensional fixed point results under (\(\psi\),\(\phi\))-contractivity conditions in the framework of \(G^*\)-metric spaces, which are spaces that result from \(G\)-metric spaces (in the sense of Z. Mustafa and B. Sims [J. Nonlinear Convex Anal. 7, No. 2, 286–297 (2006; Zbl 1111.54025)]), omitting one of their axioms. We prove that these spaces let us consider easily the product of \(G^*\)-metrics. Our result clarifies and improves some recent results on this topic because, among other different reasons, we do not need a partial order on the underlying space. Furthermore, the way in which several contractivity conditions are proposed imply that our theorems cannot be reduced to metric spaces.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E40 Special maps on metric spaces

Citations:

Zbl 1111.54025
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