On An Application of Hayashi's Inequality for Differentiable Functions
M.W. Alomari
TL;DR
This paper identifies an error in a previous proof involving Hayashi's inequality for differentiable functions, provides a correction, and introduces more general related inequalities.
Contribution
It corrects a prior proof and extends the inequalities related to Hayashi's inequality for differentiable functions.
Findings
The original proof in the referenced paper was incorrect.
A corrected proof of the main inequality is provided.
More general inequalities related to Hayashi's inequality are introduced.
Abstract
In this work, we show that the proof of the main result in [An Application of Hayashi's Inequality for Differentiable Functions, Computers & Mathematics with Applications, 32 (6) (1996), 95--99, by R.P. Agarwal and S.S. Dragomir] was wrong. A correction of the proof is given. More general related inequalities are also provided.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematics and Applications · Functional Equations Stability Results