TY - JOUR ID - 703874 TI - On algebraic bounds for exponential function with applications JO - Mathematical Analysis and its Contemporary Applications JA - MACA LA - en SN - AU - Bagul, Yogesh J. AU - Chesneau, Christophe AU - Dhaigude, Ramkrishna M. AD - Department of Mathematics, K. K. M. College, Manwath, Dist: Parbhani, Maharashtra - 431505, India AD - Department of Mathematics, University of Caen Normandie, 14000 Caen, France AD - Department of Mathematics, Government Vidarbha Institute of Science and Humanities, Amravati, Maharashtra - 444604, India Y1 - 2023 PY - 2023 VL - 5 IS - 1 SP - 85 EP - 93 KW - Algebraic bounds KW - optimal bounds KW - Exponential function KW - ratio functions DO - 10.30495/maca.2023.1987625.1068 N2 - 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. UR - https://www.macajournal.com/article_703874.html L1 - https://www.macajournal.com/article_703874_fe46e68c68825b623a5c3aea830a87fa.pdf ER -