Results 1 to 10 of about 3,546,863 (46)
Improvements of Logarithmic and Identric Mean Inequalities for Scalars and Operators
Journal of Applied Mathematics, Volume 2023, Issue 1, 2023., 2023 In this article, we provide refined inequalities for a convex Riemann’s integrable function using refinements of the classical Hermite‐Hadamard inequality. The obtained results are applied on special functions to establish new improvements of inequalities on the weighted logarithmic mean and weighted identric mean.
Aliaa Burqan +3 more
wiley +2 more sources
Sharp two-parameter bounds for the identric mean. [PDF]
J Inequal Appl, 2018 For t∈[0,1/2] $t\in [0,1/2]$ and s≥1 $s\ge 1$, we consider the two-parameter family of means Qt,s(a,b)=Gs(ta+(1−t)b,(1−t)a+tb)A1−s(a,b), $$ Q_{t,s}(a,b)=G^{s}\bigl(ta+(1-t)b,(1-t)a+tb\bigr)A^{1-s}(a,b), $$ where A and G denote the arithmetic and ...
Kouba O.
europepmc +2 more sources
Generalizations on Some Hermite‐Hadamard Type Inequalities for Differentiable Convex Functions with Applications to Weighted Means [PDF]
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 Some new Hermite‐Hadamard type inequalities for differentiable convex functions were presented by Xi and Qi. In this paper, we present new generalizations on the Xi‐Qi inequalities.
Banyat Sroysang, J.-S. Chen, T. Li
wiley +2 more sources
On Some Intermediate Mean Values [PDF]
International Journal of Mathematics and Mathematical Sciences, Volume 2013, Issue 1, 2013., 2013 We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class Λf,g(a, b) of mean values where f, g are continuously differentiable convex functions satisfying the relation f″(t) = tg″(t), t ∈ ℝ+. Then we asked for a characterization of f, g such that the inequalities H(a, b) ≤ Λf,g(a, b) ≤ A(a, b ...
Slavko Simic, Mowaffaq Hajja
wiley +2 more sources
Complete Monotonicity of Logarithmic Mean [PDF]
, 2007 In the article, the logarithmic mean is proved to be completely monotonic and an open problem about the logarithmically complete monotonicity of the extended mean values is ...
Qi, Feng
core +6 more sources
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 In this work, we introduce the idea of n–polynomial harmonically s–type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the ...
Saad Ihsan Butt +4 more
wiley +1 more source
On Strongly Convex Functions via Caputo–Fabrizio‐Type Fractional Integral and Some Applications
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator.
Qi Li +5 more
wiley +1 more source
Bounds of the Neuman-Sándor Mean Using Power and Identric Means [PDF]
, 2013 In this paper we find the best possible lower power mean bounds for the Neuman-Sándor mean and present the sharp bounds for the ratio of the Neuman-Sándor and identric ...
Yu-Ming Chu, Bo-Yong Long
core +1 more source
Schur-convexity of the Extended Mean Values [PDF]
, 2001 In this article, the Schur-convexity of the extended mean values are proved. Consequently, an inequality between the logarithmic mean values and the identity (exponential) mean values is ...
Qi, Feng
core +6 more sources
On some inequalities for the identric, logarithmic and related means [PDF]
, 2016 We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means ...
Bhayo, Barkat, Sándor, József
core +1 more source