David A. Ross’s research while affiliated with University of Hawaiʻi at Mānoa and other places

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Publications (5)


Linear equations and multiplicative polynomial equations in infinitely many variables
  • Article

December 2024

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1 Read

Communications in Algebra

Melvyn B. Nathanson

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David A. Ross


A nonstandard approach to asymptotic fixed point theorems
  • Article
  • Full-text available

December 2022

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129 Reads

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3 Citations

Journal of Fixed Point Theory and Applications

We use methods from nonstandard analysis to unify and extend results from the theory of asymptotic fixed points on metric spaces. Among the topics we consider are Kirk’s asymptotic fixed point theorem with extensions, Boyd and Wong’s fixed point theorem, and Suzuki’s fixed point theorem for asymptotic contractions of the Meier–Keeler type. We also show how Suzuki’s asymptotic contractions of the final type can be modified to yield uniform convergence on compact and bounded sets.

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Citations (2)


... Continuity of roots of a polynomial,[30,). Let f (z) be a polynomial of degree K with only simple roots. ...

Reference:

A Large-dimensional Analysis of ESPRIT DoA Estimation: Inconsistency and a Correction via RMT
Continuity of the roots of a polynomial
  • Citing Article
  • January 2024

Communications in Algebra

... The beauty of asymptotic contractions is that they are not even non-expansive and, hence, they are not iteratively equivalent to any class of contractions. However, at the same time, the most arduous part of research in this topic is to give constructive proofs of metrical fixed point theorems for this kind of mappings (see, for example, [12,17]). ...

A nonstandard approach to asymptotic fixed point theorems

Journal of Fixed Point Theory and Applications