10.30495/maca.2023.1987128.1067

Alternative proof of a monotonicity property of certain function

  1. Department of Mathematics, School of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, P. O. Box 24, Navrongo, Upper-East Region, Ghana

Published in Issue 2023-01-01

How to Cite

Alternative proof of a monotonicity property of certain function. (2023). Mathematical Analysis and Its Contemporary Applications, 5(1). https://doi.org/10.30495/maca.2023.1987128.1067

PDF views: 0

Abstract

By using L'Hospital's rule for monotonicity, we provide an alternative proof of a monotonicity property of a certain function involving the exponential function. This new approach is very concise.

Keywords

  • Monotonic function,
  • exponential function,
  • L'Hospital's rule for monotonicity,
  • hyperbolic functions

References

  1. V. S. Adamchik, Contributions to the Theory of the Barnes Function, Int. J. Math. Comput. Sci., 9(1)(2014), 11-30.
  2. J. Choi, Some mathematical constants, Appl. Math. Comput., 187(1)(2007), 122-140.
  3. B-N. Guo, A-Q. Liu and F. Qi, Monotonicity and logarithmic convexity of three functions involving exponential function, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math., 15(4)(2008), 387-392.
  4. B-N. Guo and F. Qi, Two New Proofs of the Complete Monotonicity of a Function Involving the Psi Function, Bull. Korean Math. Soc., 47(1)(2010), 103-111.
  5. A-Q. Liu, G-F. Li, B-N. Guo and F. Qi, Monotonicity and logarithmic concavity of two functions involving exponential function, Int. J. Math. Ed. Sci. Tech., 39(5)(2008), 686-691.
  6. I. Pinelis, L’hospital type Rules for Monotonicity, with Applications, J. Inequal. Pure Appl. Math., 3(1)(2002), Art No. 5, 5 pages.
  7. S-Q. Zhang, B-N. Guo and F. Qi, A Concise Proof For Properties Of Three Functions Involving The Exponential Function, Appl. Math. E-Notes, 9(2009), 177-183.