Results 1 to 10 of about 207 (55)

New properties for the Ramanujan R-function

Open Mathematics, 2022
In the article, we establish some monotonicity and convexity (concavity) properties for certain combinations of polynomials and the Ramanujan R-function by use of the monotone form of L’Hôpital’s rule and present serval new asymptotically sharp bounds ...
Cai Chuan-Yu, Chen Lu, Huang Ti-Ren, Chu Yuming   +3 more
doaj   +1 more source

Integral inequalities via harmonically h-convexity

Moroccan Journal of Pure and Applied Analysis, 2021
In this paper, we establish some estimates of the left side of the generalized Gauss-Jacobi quadrature formula for harmonic h-preinvex functions involving Euler’s beta and hypergeometric functions.
Merad Meriem, Meftah Badreddine, Souahi Abdourazek   +2 more
doaj   +1 more source

Levinson-type inequalities via new Green functions and Montgomery identity

Open Mathematics, 2020
In this study, Levinson-type inequalities are generalized by using new Green functions and Montgomery identity for the class of k-convex functions (k ≥ 3). Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points
Adeel Muhammad, Khan Khuram Ali, Pečarić Ðilda, Pečarić Josip   +3 more
doaj   +1 more source

Some new inequalities of Hermite-Hadamard type for s-convex functions with applications

Open Mathematics, 2017
In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals.
Khan Muhammad Adil, Chu Yuming, Khan Tahir Ullah, Khan Jamroz   +3 more
doaj   +1 more source

Some Identities and inequalities related to the Riemann zeta function

Moroccan Journal of Pure and Applied Analysis, 2019
A new proof of Euler’s formular for calculating ζ(2k) is given. Some new inequalities and identities for ζ(2k + 1) have also been given. The Riemann’s functional equation together with trigonometric identities were used to establish the results.
Abe-I-Kpeng Gregory, Iddrisu Mohammed Muniru, Nantomah Kwara   +2 more
doaj   +1 more source

Extensions of the Hardy‐Littlewood inequalities for Schwarz symmetrization

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 59, Page 3129-3150, 2004., 2004
For a class of functions H:(0,∞)×ℝ+2→ℝ, including discontinuous functions of Carathéodory type, we establish that ∫ℝNH(|x|,u(x),v(x))dx≤∫ℝNH(|x|,u*(x),v*(x))dx, where u*(x) and v*(x) denote the Schwarz symmetrizations of nonnegative functions u and v.
H. Hajaiej, C. A. Stuart
wiley   +1 more source

Ky Fan inequality and bounds for differences of means

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 16, Page 995-1002, 2003., 2003
We prove an equivalent relation between Ky Fan‐type inequalities and certain bounds for the differences of means. We also generalize a result of Alzer et al. (2001).
Peng Gao
wiley   +1 more source

A generalization of Ky Fan′s inequality

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 7, Page 419-425, 2001., 2001
Let Pn,r(x) be the generalized weighted means. Let F(x) be a C1 function, y = y(x) an implicit decreasing function defined by f(x, y) = 0 and 0 < m < M ≤ m′, n ≥ 2, xi ∈ [m, M], yi ∈ [m′, M′]. Then for −1 ≤ r ≤ 1, if f′x/f′y≤1, |(F(Pn,1(y))−F(Pn,r(y)))/(F(Pn,1(x))−F(Pn,r(x)))|<(maxm′≤ξ≤M′|F′(ξ)|)/(minm≤η≤M|F′(η)|)⋅M/m′⋅M/m′ A similar result exists for ...
Peng Gao
wiley   +1 more source

Spectral inequalities involving the sums and products of functions

International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 1, Page 141-157, 1982., 1980
In this paper, the notation ≺ and ≺≺ denote the Hardy‐Littlewood‐Pólya spectral order relations for measurable functions defined on a fnite measure space (X, Λ, μ) with μ(X) = a, and expressions of the form f≺g and f≺≺g are called spectral inequalities. If f, g ∈ L1(X, Λ, μ), it is proven that, for some b ≥ 0, log[b+(δfιg)+]≺≺log[b+(fg)+]≺≺log[b+(δfδg)+
Kong-Ming Chong
wiley   +1 more source