%0 Journal Article %T On algebraic bounds for exponential function with applications %J Mathematical Analysis and its Contemporary Applications %I Research & Science Group Ltd %Z 2716-9898 %A Bagul, Yogesh J. %A Chesneau, Christophe %A Dhaigude, Ramkrishna M. %D 2023 %\ 03/01/2023 %V 5 %N 1 %P 85-93 %! On algebraic bounds for exponential function with applications %K Algebraic bounds %K optimal bounds %K Exponential function %K ratio functions %R 10.30495/maca.2023.1987625.1068 %X In this paper, we establish algebraic bounds of the ratio type in nature for the natural exponential function $e^x$ involving two parameters, a and n, which become optimal as a tends to 0 or n tends to infinity. The proof is mainly based on Chebyshev's integral inequality and properties of the incomplete gamma function. Subsequently, we focus on the simple case obtained with n = 1, with comparisons to existing literature results. For the applications, we provide alternative proofs of inequalities involving ratio functions of trigonometric and hyperbolic functions. Graphics are given to illustrate the theory. %U https://www.macajournal.com/article_703874_fe46e68c68825b623a5c3aea830a87fa.pdf