• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.31-46
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• 2024

The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators _a⁺𝔍^𝜇_w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.297-306
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• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.281-288
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• 2010

By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.803-817
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• 2019

In this paper, we provide a new version of Steffensen inequality for p-calculus analogue in [17, 18] which is a generalization of previous results. Also, the conditions for validity of reverse to p-Steffensen inequalities are given. Lastly, we will obtain a generalization of p-Steffensen inequality to the case of monotonic functions.

• 대한수학회보
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• 제50권1호
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• pp.175-184
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• 2013

In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $\mathbb{R}^2$ are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.165-175
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• 2011

The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.

• 대한수학회논문집
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• 제34권2호
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• pp.573-583
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• 2019

This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Some properties for the ratio of the modified Lommel functions with the Lommel function, sinh and cosh are also discussed. As a consequence, $Tur{\acute{a}}n$ type and reverse $Tur{\acute{a}}n$ type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.623-630
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• 2009

This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.

• 대한수학회지
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• 제45권2호
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• pp.513-525
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• 2008

Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard's inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.1-9
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• 2014

We build new Hilbert-type integral inequalities in the whole plane with the non-homogeneous kernel involving some parameters and the best constant factors. We also consider their reverse.