This paper demonstrates common fixed points of Górnicki-type mappings in metric spaces, suggesting broader applications than contraction mappings.
In this article, we focus on a pair of G?rnicki-type mappings T1, T2 ? XX, (X, d) being a metric space, satisfying d(T1x, T2y) ? M[d(x, T2y) + d(y, T1x) + d(x, y)] for all x, y ? X where 0 ? M < 1. The significance of such mappings lies in their broader class compared to contraction and nonexpansive mappings. Our main focus is on the common fixed point(s) of this pair of G?rnicki-type mappings. Specifically, we establish conditions under which a couple of mappings share fixed points satisfying the aforementioned inequality. Additionally, we provide several non-trivial examples to validate our results.
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Mondal et al. (2025) studied this question.
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