Results 11 to 20 of about 329 (93)
Generalizations on some Hermite-Hadamard type inequalities for differentiable convex functions with applications to weighted means. [PDF]
ScientificWorldJournal, 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.
Sroysang B.
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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
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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
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Two sharp inequalities for Lehmer mean, identric mean and logarithmic mean [PDF]
Journal of Mathematical Inequalities, 2011 For r ∈ R , the Lehmer mean of two positive numbers a and b is defined by Lr(a,b) = ar+1 +br+1 ar +br . In this paper, we establish two sharp inequalities as follows: I(a,b) > L− 6 (a,b) and L(a,b) > L− 3 (a,b) for all a,b > 0 with a = b . Here I(a,b) = 1 e ( bb aa ) 1 b−a and L(a,b) = b−a logb−loga denote the identric mean and logarithmic mean of two ...
Ye-Fang Qiu +3 more
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A Sharp Double Inequality between Harmonic and Identric Means [PDF]
Abstract and Applied Analysis, 2011 We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa + (1 − p)b, pb + (1 − p)a) < I(a, b) < H(qa + (1 − q)b, qb + (1 − q)a) holds for all a, b > 0 with a ≠ b. Here, H(a, b), and I(a, b) denote the harmonic and identric means of two positive numbers a and b, respectively.
Yu-Ming Chu, Miao-Kun Wang, Zi-Kui Wang
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Optimal Lehmer Mean Bounds for the Combinations of Identric and Logarithmic Means [PDF]
Chinese Journal of Mathematics, 2013 For any α∈0,1, we answer the questions: what are the greatest values p and λ and the least values q and μ, such that the inequalities Lpa,b<Iαa,bL1-αa,b<Lqa,b and Lλa,b<αIa,b+1-αLa,b<Lμa,b hold for all a,b>0 with a≠b? Here, Ia,b, La,b, and Lpa,b denote the identric, logarithmic, and pth Lehmer means of two positive numbers a and b ...
Shen, Xu-Hui +2 more
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New sharp bounds for logarithmic mean and identric mean [PDF]
Journal of Inequalities and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On approximating the modified Bessel function of the first kind and Toader-Qi mean
Journal of Inequalities and Applications, 2016 In the article, we present several sharp bounds for the modified Bessel function of the first kind I 0 ( t ) = ∑ n = 0 ∞ t 2 n 2 2 n ( n ! ) 2 $I_{0}(t)=\sum_{n=0}^{\infty}\frac{t^{2n}}{2^{2n}(n!)^{2}}$ and the Toader-Qi mean T Q ( a , b ) = 2 π ∫ 0 π ...
Zhen-Hang Yang, Yu-Ming Chu
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Functional Inequalities for Generalized Complete Elliptic Integrals with Two Parameters
Journal of Function Spaces, Volume 2019, Issue 1, 2019., 2019 In this paper, we establish some functional inequalities for generalized complete elliptic integrals with two parameters, such as estimation of bounds and mean inequalities. Our main results give (p, q)‐analogues to the early results for classical complete elliptic integrals.
Xiangkai Dou +3 more
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Sharp One‐Parameter Mean Bounds for Yang Mean
Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016 We prove that the double inequality Jα(a, b) < U(a, b) < Jβ(a, b) holds for all a, b > 0 with a ≠ b if and only if α≤2/(π-2)=0.8187⋯ and β ≥ 3/2, where U(a,b)=(a-b)/[2arctan((a-b)/2ab)], and Jp(a, b) = p(ap+1 − bp+1)/[(p + 1)(ap − bp)] (p ≠ 0, −1), J0(a, b) = (a − b)/(loga − logb), and J−1(a, b) = ab(loga − logb)/(a − b) are the Yang and pth one ...
Wei-Mao Qian +3 more
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