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Tight
Exponential
Bounds For
Hyperbolic
Tangent
Yogesh J. Bagul (1), Ramkrishna M. Dhaigude
(2),
Christophe
Chesneau
*(3) and
Marko Kostić
(4)
(1) Department
of Mathematics,
K. K. M.
College, Manwath,
Dist:
Parbhani-431505,
India
Email address:
yjbagul@gmail.com
(2) Department of
Mathematics,
Government Vidarbha
Institute of Science
and
Humanities,
Amravati(M.
S.)-444604, India
Email address:
rmdhaigude@gmail.com
*(3) LMNO,
University of Caen-Normandie,
Caen, France
Email address:
christophe.chesneau@unicaen.fr
(4) Faculty of
Technical Sciences,
University of Novi
Sad, Trg D. Obradovića
6,
21125 Novi Sad,
Serbia
Email address:
marco.s@verat.net
Doi :
https://doi.org/10.47013/15.4.2
Cited by :
Jordan J. Math &
Stat.,
15 (4A) (2022),
807 - 821
PDF
Received on:
March 26,
2021;
Accepted
on: March 8,
2022
Abstract. In this
article, we aim
to obtain very
tight
exponential
bounds for the
hyperbolic
tangent
function. Our
inequalities
refine a double
inequality
recently proved
by Zhang and
Chen. In
addition,
graphical and
numerical
analysis are
carried out, and
a number of
auxiliary lemmas
may be of use on
their own.
Keywords: Hyperbolic
tangent,
sigmoidal
function,
hyperbolic
cosine,
exponential
bounds.
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