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Some majorization integral inequalities for functions defined on rectangles.

Shanhe Wu1, Muhammad Adil Khan2, Abdul Basir2

  • 11Department of Mathematics, Longyan University, Longyan, China.

Journal of Inequalities and Applications
|July 17, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a new integral majorization theorem for functions on rectangles. This theorem establishes novel integral inequalities, generalizing existing results like weighted Favard's inequality.

Keywords:
Convex functionCoordinate convex functionFavard’s inequalityMajorizationRectangle

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Area of Science:

  • Mathematical Analysis
  • Inequalities

Background:

  • Integral inequalities are fundamental in mathematical analysis.
  • Previous work by Maligranda et al. established important results in this area.

Purpose of the Study:

  • To prove a novel integral majorization theorem.
  • To establish new integral inequalities for functions defined on rectangles.
  • To generalize existing inequalities, including weighted Favard's inequality.

Main Methods:

  • Development of a new integral majorization theorem.
  • Application of the theorem to derive new integral inequalities.
  • Comparison with existing inequalities, such as weighted Favard's inequality.

Main Results:

  • A new integral majorization theorem for functions on rectangles is proven.
  • New integral inequalities are established for functions defined on rectangles.
  • The derived inequalities generalize weighted Favard's inequality and prior results.

Conclusions:

  • The study provides a significant advancement in the theory of integral inequalities.
  • The new theorem and inequalities offer broader applicability and deeper insights.
  • This work extends and refines existing mathematical knowledge in the field.