Next Article in Journal
On Some Important Dynamic Inequalities of Hardy–Hilbert-Type on Timescales
Next Article in Special Issue
Some Companions of Fejér-Type Inequalities for Harmonically Convex Functions
Previous Article in Journal
On a Fractional Parabolic Equation with Regularized Hyper-Bessel Operator and Exponential Nonlinearities
Previous Article in Special Issue
Some Rational Approximations and Bounds for Bateman’s G-Function
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 14
Issue 7
10.3390/sym14071420
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l)

by
Omelsaad Ahfaf
1,
Ahmed Talat
2 and
Mansour Mahmoud
3,*
1
Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2
Mathematics and Computer Sciences Department, Faculty of Science, Port Said University, Port Said 42526, Egypt
3
Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2022, 14(7), 1420; https://doi.org/10.3390/sym14071420
Submission received: 4 June 2022 / Revised: 27 June 2022 / Accepted: 8 July 2022 / Published: 11 July 2022
(This article belongs to the Special Issue Mathematical Inequalities, Special Functions and Symmetry)
Versions Notes

Abstract

Symmetrical patterns exist in the nature of inequalities, which play a basic role in theoretical and applied mathematics. In several studies, inequalities present accurate approximations of functions based on their symmetry properties. In the paper, we prove the completely monotonic (CM) property of some functions involving the function Δ(l)=ψ″(l)+ψ′(l)2 and hence we deduce a new double inequality for it. Additionally, we study the CM degree of some functions involving the function ψ′(l). Our new bounds takes priority over some of the recently published results.
Keywords: tri-gamma; tetra-gamma; CM function; CM degree; inequality tri-gamma; tetra-gamma; CM function; CM degree; inequality

Share and Cite

MDPI and ACS Style

Ahfaf, O.; Talat, A.; Mahmoud, M. Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l). Symmetry 2022, 14, 1420. https://doi.org/10.3390/sym14071420

AMA Style

Ahfaf O, Talat A, Mahmoud M. Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l). Symmetry. 2022; 14(7):1420. https://doi.org/10.3390/sym14071420

Chicago/Turabian Style

Ahfaf, Omelsaad, Ahmed Talat, and Mansour Mahmoud. 2022. "Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l)" Symmetry 14, no. 7: 1420. https://doi.org/10.3390/sym14071420

APA Style

Ahfaf, O., Talat, A., & Mahmoud, M. (2022). Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l). Symmetry, 14(7), 1420. https://doi.org/10.3390/sym14071420

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop