Results 21 to 30 of about 586 (111)

Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications

Journal of Inequalities and Applications
In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of
László Horváth
doaj   +3 more sources

Exact Solutions of Three Types of Conformable Fractional-Order Partial Differential Equations.

Comput Intell Neurosci, 2022
Fractional calculus is widely used in biology, control systems, and engineering, so it has been highly valued by scientists. Fractional differential equations are considered an important mathematical model that is widely used in science and technology to describe physical phenomena more accurately in terms of time memory and spatial interactions.
Ma L.
europepmc   +2 more sources

Improvements of Jensen-Type Inequalities for Diamond-α Integrals. [PDF]

Int Sch Res Notices, 2014
We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left‐hand side and the right‐hand ...
Bibi R, Pečarić J, Lipanović MR.
europepmc   +2 more sources

The Hermite–Hadamard–Mercer Type Inequalities via Generalized Proportional Fractional Integral Concerning Another Function

International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022
In order to be able to study cosmic phenomena more accurately and broadly, it was necessary to expand the concept of calculus. In this study, we aim to introduce a new fractional Hermite–Hadamard–Mercer’s inequality and its fractional integral type inequalities.
Tariq A. Aljaaidi, Deepak B. Pachpatte, Ram N. Mohapatra   +2 more
wiley   +1 more source

Bounds for the Jensen Gap in terms of Power Means with Applications

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
Jensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two sides of Jensen’s inequality in terms of power means. An
Xuexiao You, Muhammad Adil Khan, Hamid Reza Moradi, Muhammad Arif   +3 more
wiley   +1 more source

Uniform Treatment of Jensen’s Inequality by Montgomery Identity

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n−convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite–Hadamard inequality.
Tahir Rasheed, Saad Ihsan Butt, Đilda Pečarić, Josip Pečarić, Ahmet Ocak Akdemir, Xiaolong Qin   +5 more
wiley   +1 more source

Extended Jensen’s Functional for Diamond Integral via Hermite Polynomial

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
In this paper, with the help of Hermite interpolating polynomial, extension of Jensen’s functional for n‐convex function is deduced from Jensen’s inequality involving diamond integrals. Special Hermite conditions, including Taylor two‐point formula and Lagrange’s interpolation, are also deployed to find further extensions of Jensen’s functional.
Rabia Bibi, Fazilat Bibi, Ammara Nosheen, Josip Pečarić, Andrea Scapellato   +4 more
wiley   +1 more source

On the refinements of the integral Jensen-Steffensen inequality [PDF]

Journal of Inequalities and Applications, 2013
Dans cet article, nous présentons des versions intégrales de certains résultats récemment prouvés qui affinent l'inégalité de Jensen-Steffensen. Nous prouvons la convexité n-exponentielle et la log-convexité des fonctions associées aux fonctions linéaires construites à partir des inégalités raffinées et prouvons également la propriété de monotonie des ...
Sadia Khalid, Josip ‎Pečarić
openaire   +2 more sources

Jensen-Steffensen's and related inequalities for superquadratic functions [PDF]

Mathematical Inequalities & Applications, 2008
Refinements of Jensen-Steffensen's inequality, Slater-Pečarić's inequality and majorization theorems for superquadratic functions are presented.
Abramovich, Shoshana, Banić, Senka, Matić, Marko, Pečarić Josip   +3 more
openaire   +3 more sources

The Jensen-Steffensen inequality [PDF]

Mathematical Inequalities & Applications, 1998
New proofs of the Jensen-Steffensen and its inverse inequality given by the reviewer are presented.
openaire   +2 more sources