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Some Ostrowski type inequalities for the Riemann–Stieltjes integral for various classes of integrands and integrators are surveyed. Applications for the midpoint rule and a generalised trapezoidal type rule are also presented.
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By employing Mawhin's continuation theorem, the existence of periodic solutions of the p-Laplacian generalized Lienard equation with deviating argument... more
By employing Mawhin's continuation theorem, the existence of periodic solutions of the p-Laplacian generalized Lienard equation with deviating argument (ϕp(x′(t)))′+f(t,x(t))x′(t)+β(t)g(x(t-τ(t)))=e(t)(ϕp(x′(t)))′+f(t,x(t))x′(t)+β(t)g(x(t-τ(t)))=e(t) under various assumptions are obtained.
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For given real numbers a≥ 0, b∈ ℝ and c∈ ℝ, let F a, b, c (x)=[Γ (x+ 1)] 1/x (1+ a/x) x+ b/xc and φ a, b, c (x)= ψ ″(x)+[2+(b+ c) x− 2 x 2]/x 3+[3 a (2 a− b)+(6 a− b) x+ 2 x 2]/(x+ a) 3 with x∈(0,∞), where Γ (x) and ψ (x) are the... more
For given real numbers a≥ 0, b∈ ℝ and c∈ ℝ, let F a, b, c (x)=[Γ (x+ 1)] 1/x (1+ a/x) x+ b/xc and φ a, b, c (x)= ψ ″(x)+[2+(b+ c) x− 2 x 2]/x 3+[3 a (2 a− b)+(6 a− b) x+ 2 x 2]/(x+ a) 3 with x∈(0,∞), where Γ (x) and ψ (x) are the well-known Euler gamma function and the psi or ...
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Abstract In this paper some new integrodifferential inequalities of the Gronwall and Wendroff type in several independent variables are established. These inequalities are useful in the study of many qualitative as well as quantitative... more
Abstract In this paper some new integrodifferential inequalities of the Gronwall and Wendroff type in several independent variables are established. These inequalities are useful in the study of many qualitative as well as quantitative properties of solutions of partial differential and integral equations.
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Summary In this paper some new integral inequalities of the Sobolev type involving many functions of many variables are established. These in turn can be used to serve as generators of other integral inequalities.
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Summary In this paper we establish some new Opial-type inequalities in two variables which have a wide range of applications in the study of differential and integral equations.
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We give a new Hermite–Hadamard inequality for a function f:[a,b]×[c,d]⊂ℝ2→ℝ which is semiconvex of rate (k1,k2) on the coordinates. This generalizes some existing results on Hermite–Hadamard inequalities of S. S. Dragomir. In addition, we... more
We give a new Hermite–Hadamard inequality for a function f:[a,b]×[c,d]⊂ℝ2→ℝ which is semiconvex of rate (k1,k2) on the coordinates. This generalizes some existing results on Hermite–Hadamard inequalities of S. S. Dragomir. In addition, we explain the Hermite–Hadamard inequality from the point of view of optimal mass transportation with cost function c(x,y):=f(y−x)+k12|x1−y1|2+k22|x2−y2|2, where f(⋅):[a,b]×[c,d]→[0,∞) is semiconvex of rate (k1,k2) on the coordinates and x=(x1,x2), y=(y1,y2)∈[a,b]×[c,d].
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In the present paper, we establish some new Opial’s type inequalities involving higher-order partial derivatives. Our results provide new estimates on inequalities of these type.
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ABSTRACT In this paper, we establish Lp-Aleksandrov–Fenchel inequality. As applications, we prove a new Brunn–Minkowski type inequality and generalize some interrelated results.