Nieto-Lopez theorems in ordered metric spaces
Mihai Turinici
TL;DR
This paper demonstrates that the comparison type fixed point results in ordered metric spaces by Nieto and Rodriguez-Lopez are special cases of the classical Banach contraction principle, unifying these concepts.
Contribution
It shows that the fixed point theorems in ordered metric spaces by Nieto and Rodriguez-Lopez are particular instances of Banach's contraction principle, clarifying their relationship.
Findings
Fixed point results are special cases of Banach's contraction principle.
Unified understanding of fixed point theorems in ordered metric spaces.
Simplifies the theoretical landscape of fixed point results.
Abstract
The comparison type version of the fixed point result in ordered metric spaces established by Nieto and Rodriguez-Lopez [Acta Math. Sinica (English Series), 23 (2007), 2205-2212] is nothing but a particular case of the classical Banach's contraction principle [Fund. Math., 3 (1922), 133-181].
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Taxonomy
TopicsFixed Point Theorems Analysis · Nonlinear Differential Equations Analysis · Optimization and Variational Analysis