In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）...In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.展开更多
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for...Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.展开更多
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t...The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.展开更多
In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.
In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshe...In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.展开更多
文摘In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
文摘Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.
文摘The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.
基金The NSF (10571040) of ChinaNSF (L2010Z02) of Hebei Normal University
文摘In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.
基金the Special Funds for Major State Basic Research Projects (Grant No.G19990328) National Science Foundation of China (Grant No.10471128)
文摘In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.
