Integral Inequalities Involving Strictly Monotone Functions

Mohamed Jleli and Bessem Samet ()
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Mohamed Jleli: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Bessem Samet: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 8, 1-14

Abstract: Functional inequalities involving special functions are very useful in mathematical analysis, and several interesting results have been obtained in this topic. Several methods have been used by many authors in order to derive upper or lower bounds of certain special functions. In this paper, we establish some general integral inequalities involving strictly monotone functions. Next, some special cases are discussed. In particular, several estimates of trigonometric and hyperbolic functions are deduced. For instance, we show that Mitrinović-Adamović inequality, Lazarevic inequality, and Cusa-Huygens inequality are special cases of our obtained results. Moreover, an application to integral equations is provided.

Keywords: integral inequalities; strictly monotone functions; functional inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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