In this paper, we introduce a class of generalized vector equilibrium problems for set-valued mappings which include a number of vector equilibrium problems, generalized vector variational-like inequality problems and generalized vector variational inequality problems as special cases. By using the KKM-Fan theorem and Nadler’s lemma, we prove the existence of solution to this class of generaliz...

We have studied some new generalizations of Hardy's integral inequality using the generalized Holder's inequality.

This paper presents and characterizes a two-parameter class of inequality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group inequality terms using a ge...

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...

In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke’s generalized directional derivative in reflexive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke’s generalized directional derivative under different monotonicity assumptions, we establish two kinds of co...

We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler ~‘‘Schwarzschild–anti-de Sitter’’! solution, within ~mainly! a conformal framework. We show connectedness of conformal infinity for appropriately regular such spacetimes. We give an explicit expression for the Hamiltonian ma...