Results 81 to 90 of about 311,275 (193)

Norm inequalities for weighted power means of operators

Linear Algebra and its Applications, 2002
Let \(A_{i}\), \(X_{i}\) and \(Y_{i}\) be bounded linear operators on a Hilbert space for \(i=1,2,\dots ,n\). In the present paper, the authors prove the following norm inequalities: (i) If \(\sum_{i=1}^{n}X^{*}_{i}X_{i}\leq I\), \(\sum_{i=1}^{n}Y^{*}_{i}Y_{ i}\leq I\) and \(r\geq 1\), then \[ \Bigg|\Bigg|\Bigg|\Bigg |\sum_{i =1}^{n} X_{i}^{*}A_{i}Y_{i}
Hirzallah, Omar, Kittaneh, Fuad
openaire   +1 more source

New Hadamard-type inequalities for E-convex functions involving generalized fractional integrals

Journal of Inequalities and Applications, 2022
In this article, we establish some new Hadamard-type inequalities for E-convex functions involving generalized fractional integrals. These inequalities include a generalized Hadamard-type inequality and the corresponding right Hadamard-type inequalities ...
Asia Latif, Rashida Hussain
doaj   +1 more source

Some fractional Hermite–Hadamard-type integral inequalities with s- ( α , m ) $(\alpha,m)$ -convex functions and their applications

Advances in Difference Equations, 2021
Under the new concept of s- ( α , m ) $(\alpha,m)$ -convex functions, we obtain some new Hermite–Hadamard inequalities with an s- ( α , m ) $(\alpha,m)$ -convex function.
R. N. Liu, Run Xu
doaj   +1 more source

Some New Improvements for Fractional Hermite–Hadamard Inequalities by Jensen–Mercer Inequalities

Journal of Function Spaces
This article’s objective is to introduce a new double inequality based on the Jensen–Mercer JM inequality, known as the Hermite–Hadamard–Mercer inequality. We use the JM inequality to build a number of generalized trapezoid-type inequalities.
Maryam Gharamah Ali Alshehri, Abd-Allah Hyder, Hüseyin Budak, Mohamed A. Barakat   +3 more
doaj   +1 more source

A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

Mathematics
Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques.
Moin-ud-Din Junjua, Ather Qayyum, Arslan Munir, Hüseyin Budak, Muhammad Mohsen Saleem, Siti Suzlin Supadi   +5 more
doaj   +1 more source

Advancements in Harmonic Convexity and Its Role in Modern Mathematical Analysis

Journal of Mathematics
Convex functions play an integral part in artificial intelligence by providing mathematical guarantees that make optimization more efficient and reliable.
Sabila Ali, Muhammad Samraiz, Saima Naheed, Miguel Vivas-Cortez   +3 more
doaj   +1 more source

More results on integral inequalities for strongly generalized (ϕ,h,s) $( \phi,h,s )$-preinvex functions

Journal of Inequalities and Applications, 2019
The main goal of this research is to introduce a new form of generalized Hermite–Hadamard and Simpson type inequalities utilizing Riemann–Liouville fractional integral by a new class of preinvex functions which is known as strongly generalized (ϕ,h,s) $(
Shahid Qaisar, Jamshed Nasir, Saad Ihsan Butt, Sabir Hussain   +3 more
doaj   +1 more source

Optimal Power Mean Bounds for the Weighted Geometric Mean of Classical Means

, 2010
For , the power mean of order of two positive numbers and is defined by , for , and , for . In this paper, we answer the question: what are the greatest value and the least value such that the double inequality holds for all and with ?
B. Long, Y. Chu
semanticscholar   +1 more source

Some inequalities for weighted power mean

Journal of Mathematical Inequalities
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean

, 2011
For 1 𝑟 + ∞ , we find the least value 𝛼 and the greatest value 𝛽 such that the inequality 𝐻 𝛼 ( 𝑎 , 𝑏 ) 𝐴 𝑟 ( 𝑎 , 𝑏 ) 𝐻 𝛽 ( 𝑎 , 𝑏 ) holds for all 𝑎 , 𝑏 > 0 with 𝑎 ≠ 𝑏 .
Hongya Gao, Jianling Guo, Yu Wang
semanticscholar   +1 more source