By using the way of weight functions and technique of real analysis, a new multiple half-discrete Hilbert-type inequality with the best constant factor is given. As applications, the equivalent forms, operator expressions as well as some reverse inequalities are also considered. Mathematics subject classification (2010): 26D15, 47A07.

* Correspondence: bcyang@gdei. edu.cn Department of Mathematics, Guangdong University of Education Guangzhou, Guangdong 510303, P. R. China Full list of author information is available at the end of the article Abstract Using the way of weight functions and the technique of real analysis, a half-discrete Hilbert-type inequality with a general homogeneous kernel is obtained, and a best extension...

In this paper we review previous work on non modal spatial logics and explore a corresponding modal spatial logic. Furthermore we present an initial classication of kinds of spatially indexed propositions.

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...

The notion of a 1-vertex transfer matrix for multidimensional codes. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method ...

In this paper, we prove unique fixed point theorem for weakly inward contractions on 2-Banach space and introduce the concept of fixed point curve in 2-Banach space. 2010 AMS Classication: 41A65, 46B20,47H10, 54H25.