Results 71 to 80 of about 36,362 (173)

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
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A note on the proofs of generalized Radon inequality [PDF]

Mathematica Moravica, 2018
In this paper, we introduce and prove several generalizations of the Radon inequality. The proofs in the current paper unify and also are simpler than those in early published work.
Yongtao Li, Xian-Ming Gu, Xiao Jianci
doaj  

Matrix power means and Pólya-Szegő type inequalities

Surveys in Mathematics and its Applications, 2020
Summary: It is shown that, if \(\mu\) is a compactly supported probability measure on \(\mathbb{M}^+_n\), then, for every unit vector \(\eta\in\mathbb{C}^n\), there exists at compactly supported probability measure (denoted by \(\langle\mu\eta,\eta\rangle)\) on \(\mathbb{R}^+\) so that the inequality \[\langle P_t(\mu)\eta,\eta\rangle\le P_t(\langle\mu
Mohsen Kian, Fatemeh Rashid
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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

Some results on integral inequalities via Riemann–Liouville fractional integrals

Journal of Inequalities and Applications, 2019
In current continuation, we have incorporated the notion of s−(α,m) $s- ( {\alpha,m} ) $-convex functions and have established new integral inequalities. In order to generalize Hermite–Hadamard-type inequalities, some new integral inequalities of Hermite–
Xiaoling Li, Shahid Qaisar, Jamshed Nasir, Saad Ihsan Butt, Farooq Ahmad, Mehwish Bari, Shan E Farooq   +6 more
doaj   +1 more source

Strengthened power mean inequalities based on superquadraticity

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
The main goal of this paper is a study of more precise power mean inequalities based on a superquadraticity. Our main results lean on a strengthened form of the Jensen inequality that holds for a class of non-negative superquadratic functions. In addition, even more accurate class of power mean inequalities has been established by using the invariance ...
Bošnjak, Marija, Krnić, Mario
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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

Generalization and sharpness of the power means inequality and their applications

Journal of Mathematical Analysis and Applications, 2005
The main results of the paper sharpen the classical well-known inequalities between power means. As a consequence, the inequality \[ \left(\sum_{i=1}^n x_i\right)^n \leq (n-1)^{n-1} \sum_{i=1}^n x_i^n + n\big(n^{n-1}-(n-1)^{n-1}\big)\prod_{i=1}^n x_i \] is proved for all \(x_1,\dots,x_n>0\), \(n\geq2\), which was conjectured by \textit{W. Janous, M. K.
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Complementary inequalities to Davis-Choi-Jensen's inequality and operator power means

, 2021
Let $f$ be an operator convex function on $(0,\infty)$, and $Φ$ be a unital positive linear maps on $B(H)$. we give a complementary inequality to Davis-Choi-Jensen's inequality as follows \begin{equation*} f(Φ(A))\geq \frac{4R(A,B)}{(1+R(A,B))^2}Φ(f(A)), \end{equation*} where $R(A, B)=\max\{r(A^{-1}B) ,r(B^{-1}A)\}$ and $r(A)$ is the spectral radius of
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Optimal inequalities between Seiffert's mean and power means [PDF]

Mathematical Inequalities & Applications, 2004
For the Seiffert mean \(P(x,y):=(x-y)/[4\arctan (\sqrt{x/y})-\pi ]\), the author proves that the evaluation \(A_{p}\leq P\leq A_{q}\) holds if and only if ...
openaire   +2 more sources