Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.
GENERALIZATION OF HILBERT AND HARDY-HILBERT INTEGRAL INEQUALITIES
The main objective of this paper is a study of some new generalizations of Hilbert's and Hardy-Hilbert's type inequalities. We establish general form of multiple Hilbert-type inequality and we also introduce multiple inequality of Hardy-Hilbert type. Further, the best possible constants are obtained for some general cases.
Convergence Anatomization of Aquaculture Production in Leading Fish-Producing Countries During the Period of 1997-2013
Growth and national importance of aquaculture production is empirically assessed as an important indicator of development. The present article aims to test whether the major aquaculture producing countries of the world are converging over time. The authors have applied the absolute and conditional beta convergence and sigma convergence approaches on the data of FAO for the period 1997-2013. The results show that there is an absolute beta convergence and sigma convergence among 25 major aquaculture producing countries; negative sign of coefficient of conditional beta convergence with per capita income is also noticed. It implies, the growth rates of aquaculture for developed nations are declining with rise in per capita income and backward fish-intensive countries are catching up with the giant producers like China and India. The cross-country variations are also going down which means that the countries' development gaps are getting narrowed by means of growth of aquaculture resources.