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Integral inequalities under beta function and preinvex type functions.

Izhar Ahmad1

  • 1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261 Saudi Arabia.

Springerplus
|May 18, 2016
PubMed
Summary

This study introduces P-preinvex functions and establishes new integral inequalities involving the beta function. These findings extend existing mathematical literature on inequalities.

Keywords:
Euler beta functionHolder’s inequalityIntegral inequalityP-preinvex function

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Area of Science:

  • Mathematical Analysis
  • Optimization Theory

Background:

  • P-preinvex functions are a generalization of convex functions.
  • Integral inequalities are fundamental in various mathematical fields.

Purpose of the Study:

  • To introduce the concept of P-preinvex functions.
  • To establish new integral inequalities utilizing P-preinvex functions and the beta function.
  • To extend and generalize existing results in the literature.

Main Methods:

  • Introduction of the P-preinvex function definition.
  • Application of integral inequality techniques.
  • Utilizing properties of the beta function.

Main Results:

  • The paper establishes novel integral inequalities for P-preinvex functions.
  • New inequalities involving the beta function are derived.
  • The results generalize and improve upon previously known inequalities.

Conclusions:

  • The introduction of P-preinvex functions provides a new framework for inequality research.
  • The established integral inequalities offer valuable tools for mathematical analysis.
  • This work contributes to the advancement of the theory of convex and preinvex functions.