Completely monotonic functions involving Bateman’s G−function

Mansour Mahmoud; Ahmed Talat; Hesham Moustafa; Ravi P. Agarwal

Completely monotonic functions involving Bateman’s G−function

Authors

Mansour Mahmoud Mansoura University, Faculty of Science, Mathematics Department, Mansoura 35516, Egypt. https://orcid.org/0009-0005-3174-762X
Ahmed Talat Port Said University, Faculty of Science, Mathematics and Computer Sciences Department, Port Said, Egypt. https://orcid.org/0009-0005-3174-762X
Hesham Moustafa Mansoura University, Faculty of Science, Mathematics Department, Mansoura 35516, Egypt. https://orcid.org/0009-0005-3174-762X
Ravi P. Agarwal Department of Mathematics, Texas A&M University-Kingsville, Texas 78363, USA https://orcid.org/0009-0005-3174-762X

Keywords:

Bateman’s G−function, completely monotonic, best possible constant, Bernoulli numbers, Wallis ratio, hyperbolic tangent function.

Abstract

n this paper, we prove the complete monotonicity of some functions involving Bateman’s G−function and show that where α = 1 and β = 0 are the best possible constants, which is a refinement of a recent result. Then, we give a new proof of Slavi´c inequality about Wallis ratio Wm and provide a new inequality for Wm. Our new inequality improves some recent related works. We also present two inequalities for the hyperbolic tangent function.

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Published

2021-10-16

How to Cite

Mansour Mahmoud, Ahmed Talat, Hesham Moustafa, & Ravi P. Agarwal. (2021). Completely monotonic functions involving Bateman’s G−function. Journal of Computational Analysis and Applications (JoCAAA), 29(5), 970–986. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/207