Results 31 to 40 of about 460 (101)

Sharp Gautschi inequality for parameter 0

, 2017
In the article, we present the best possible parameters a,b on the interval (0,∞) such that the Gautschi double inequality [(xp +a) − x]/a < ex ∫ ∞ x e−t p dt < [(xp +b) − x]/b holds for all x > 0 and p ∈ (0,1) .
Zhen-Hang Yang, E. Zhang, Y. Chu
semanticscholar   +1 more source

Ostrowski and trapezoid type inequalities for Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives

Fractional Differential Calculus, 2020
In this paper we establish some Ostrowski and trapezoid type inequalities for the Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives.
S. Dragomir
semanticscholar   +1 more source

On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals

, 2013
In this paper, three fundamental and important Riemann-Liouville fractional integral identities including a twice differentiable mapping are established. Secondly, some interesting Hermite-Hadamard type inequalities involving Riemann-Liouville fractional
Yuruo Zhang, Jinrong Wang
semanticscholar   +1 more source

On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities

, 2010
Recently trigonometric inequalities of N. Cusa and C. Huygens (see, e.g., [9]), J. Wilker [11], and C. Huygens [4] have been discussed extensively in mathematical literature.
E. Neuman, J. Sándor
semanticscholar   +1 more source

A completely monotonic function involving the tri- and tetra-gamma functions

, 2010
The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function.
Guo, Bai-Ni, Qi, Feng
core   +1 more source

SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE FOR s-CONVEX FUNCTIONS

, 2015
Some new results related of the left-hand side of the Hermite-Hadamard type inequal- ities for the class of mappings whose second derivatives at certain powers are s convex in the second sense are established.
M. Sarıkaya, Mehmet Ey, Up Kiris
semanticscholar   +1 more source

Sharp lower and upper bounds for the q-gamma function

, 2020
This paper is devoted to provide sharp bounds for the q -gamma function from below and above for all q > 0 by means of investigating the monotonicity property to analytical functions involving logarithm q -gamma function.
A. Salem
semanticscholar   +1 more source

Best bounds for the Lambert W functions

Journal of Mathematical Inequalities, 2020
This paper is devoted to provide tractable closed-form upper and lower bounds for the two real branches of the Lambert W function W(z(t)) for all positive real variable t where z(t) is increasing function on (0,∞) and bounded by zero and −e−1 ...
A. Salem
semanticscholar   +1 more source

A harmonic mean inequality for the polygamma function

, 2020
In this work, we discuss some new inequalities and a concavity property of the polygamma function ψ (n)(x) = dn dxn ψ(x) , x > 0 , where ψ(x) represents the digamma function (i.e. logarithmic derivative of the gamma function Γ(x) ).
Sourav Das, A. Swaminathan
semanticscholar   +1 more source

Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem [PDF]

, 2009
In the expository review and survey paper dealing with bounds for the ratio of two gamma functions, along one of the main lines of bounding the ratio of two gamma functions, the authors look back and analyze some known results, including Wendel’s ...
Feng Qi (祁锋), Qiu-Ming Luo
semanticscholar   +1 more source