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Inequalities on an extended Bessel function.

Rosihan M Ali1, See Keong Lee1, Saiful R Mondal2

  • 11School of Mathematical Sciences, Universiti Sains Malaysia, USM Penang, Malaysia.

Journal of Inequalities and Applications
|April 3, 2018
PubMed
Summary

This study introduces new formulations for an extended Bessel function, deriving its differential equation and establishing novel functional inequalities and monotonicity properties. The research also explores log-concavity and log-convexity for related functions, yielding Turán-type inequalities.

Keywords:
Bessel functionGeneralized Bessel functionLog-convexityMonotonicity propertiesTurán-type inequality

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Area of Science:

  • Mathematical Analysis
  • Special Functions

Background:

  • Extended Bessel functions are crucial in various scientific and engineering fields.
  • Understanding their properties, including differential equations and inequalities, is essential for advanced applications.

Purpose of the Study:

  • To derive novel representation formulations for an extended Bessel function.
  • To establish functional inequalities and investigate monotonicity properties.
  • To explore log-concavity/convexity and Turán-type inequalities for related functions.

Main Methods:

  • Derivation of representation formulations using parameters a, b, and p.
  • Analysis of differential equations satisfied by the extended Bessel function.
  • Investigation of functional inequalities, monotonicity, log-concavity, and log-convexity.

Main Results:

  • New representation formulations for the extended Bessel function were obtained.
  • An [Formula: see text]-order differential equation for the function was derived.
  • Functional inequalities, monotonicity properties, and Turán-type inequalities were established.

Conclusions:

  • The study provides a comprehensive analysis of an extended Bessel function and its related properties.
  • The derived inequalities and differential equations offer valuable tools for further research in special functions and applied mathematics.