On a paper of \v{Z}. Tomovski and R. Hilfer
Viktor P. Zastavnyi
TL;DR
This paper critically examines a previous proof of inequalities for alternating Mathieu type series, identifying errors and clarifying the parameter ranges where the inequalities do not hold.
Contribution
It corrects a mistake in the earlier proof and specifies the parameter values for which the inequalities are invalid.
Findings
Identified errors in the original proof.
Determined parameter ranges where inequalities fail.
Clarified the validity conditions for the inequalities.
Abstract
The proof of the inequalities for alternating Mathieu type series in Journal of Mathematical Inequalities (2008) by \v{Z}. Tomovski and R. Hilfer contains a mistake. Here we give the values of parameters for which these inequalities are not true.
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Taxonomy
TopicsMathematical functions and polynomials · Functional Equations Stability Results · Meromorphic and Entire Functions