On Bullen's and related inequalities
Ana Maria Acu, Heiner Gonska
TL;DR
This paper extends Bullen's inequality for continuous functions using the second order modulus of smoothness, introduces a new form via the least concave majorant, and explores the composite case.
Contribution
It provides new extensions and forms of Bullen's inequality for continuous functions, including the composite case, using advanced mathematical tools.
Findings
Extended Bullen's inequality for continuous functions.
Derived a new form using the least concave majorant.
Analyzed the composite case of Bullen's inequality.
Abstract
The estimate in Bullen's inequality will be extended for continuous functions using the second order modulus of smoothness. A different form of this inequality will be given in terms of the least concave majorant. Also, the composite case of Bullen's inequality is considered.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Mathematical Inequalities and Applications · Optimization and Variational Analysis