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New approximation inequalities for circular functions.

Ling Zhu1, Marija Nenezić2

  • 11Department of Mathematics, Zhejiang Gongshang University, Hangzhou City, China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

This study presents improved exponential approximation inequalities for specific functions. These findings utilize Bernoulli numbers and new criteria for power series monotonicity.

Keywords:
Bernoulli numbersCircular functionsExponential approximation inequalitiesMitrinovic–Adamovic inequality

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Area of Science:

  • Mathematical Analysis
  • Approximation Theory

Background:

  • Exponential approximation inequalities are crucial in various mathematical fields.
  • Understanding the behavior of functions using series expansions is a fundamental area of research.

Purpose of the Study:

  • To derive improved exponential approximation inequalities for two specific functions.
  • To establish new criteria for the monotonicity of the quotient of two power series.

Main Methods:

  • Utilizing the properties of Bernoulli numbers.
  • Developing and applying new criteria for the monotonicity of quotient of two power series.

Main Results:

  • Obtained improved exponential approximation inequalities for the functions and .
  • Demonstrated the effectiveness of the new criteria for power series monotonicity.

Conclusions:

  • The derived inequalities offer enhanced approximations for the studied functions.
  • The new monotonicity criteria provide a valuable tool for analyzing power series.