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While the existence or lack of existence of fixed points in dynamic systems often depend on the topological or set-theoretic order structure of the mapping, Abian (1968) [4] proved a fixed point theorem for finite sets that does not rely on any such structure.b This note relates this theorem of Abian with the assumption of isotone mappings.
The uniqueness is obtained by imposing some order theoretic conditions additionally.
There is a blending of analytic and order theoretic approaches in the proofs.
Several metric and order theoretic concepts are utilized in our results.
Separate order theoretic condition are imposed to ensure the uniqueness of the best proximity point in the main result.
We adopt an information theoretic approach in order to quantify the informational content of the microstructural details and find ways to condense it while assessing quantitatively the approximation introduced.
In this work, we adopt a cooperative game theoretic approach in order to tackle the social ridesharing (SR) problem, where a set of commuters, connected through a social network, form coalitions and arrange one-time rides at short notice.
Note, that this is a completely theoretic assumption in order to illustrate the occurring problems regarding the most simple scenario.
The related literature on optimal pricing and (R, Q) in the supply chain regarding lead time and service level can be categorized into two groups: up-to-level policy (R, Q) and game theoretic pricing and ordering decisions.
In 1975 there were so few people working in fixed point theory that at that time the theory had not separated into two branches - 'metric' and 'topological-order theoretic'.
Since the validity of formulas like $\forall x \ Px \rightarrow \exists x Px$ or $\exists x (Px \rightarrow Px)$ is largely a byproduct of what may strike one as an ad hoc stipulation, one may be motivated to expand the range of model-theoretic interpretations in order to allow for a model with an empty domain of discourse.
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