Generalization of two-dimensional Hardy type inequality for fuzzy integrals

Abstract

In this paper, a new two-dimensional Hardy type inequality is given in terms of pseudo-analysis dealing with set-valued functions. The first one is given for a pseudo-integral of set-valued function where pseudo-addition and pseudo-multiplication are constructed by a monotone continuous function $g:[0,\infty ]\to [0,\infty ]$. Another is given by the semiring $([0,1],\max ,\odot )$ where pseudo-multiplication is generated by an increasing continuous function.