In this paper, a class of generalized general mixed quasi variational inequalities is introduced and studied. We prove the existence of the solution of the auxiliary problem for the generalized general mixed quasi variational inequalities, suggest a predictor-corrector method for solving the generalized general mixed quasi variational inequalities by using the auxiliary principle technique. If ...

The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green's functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green's functions. As an application, we formulate the monotonicity of linear functionals construc...

We generalize some results due to Pappalardo and Passacantando [10]. We prove necessary and sufficient conditions for the monotonicity of a trajectory of an autonomous dynamical system with locally Lipschitz data, by means of Clarke’s generalized Jacobian. Some of the results are developed in the framework of variational inequalities.

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered.  2005 Elsevier Inc. All...

This article presents an approach to generalized convex duality theory based on Fenchel-Moreau conjugations; in particular, it discusses quasiconvex conjugation and duality in detail. It also describes the related topic of microeconomics duality and analyzes the monotonicity of demand functions.

For a ? (0,1/2] and r (0,1), let Ka(r) (K (r)) denote the generalized elliptic integral (complete integral, respectively) of first kind. In this article, we mainly present sufficient necessary condition under which function [K(r)-Ka(r)]=(1-2a)?(?? R) is monotone on (0,1/2) for each fixed (0,1). The obtained result leads to conclusion that inequality K (r)- (1-2a)? [K(r)- ?/2] (r)-(1-2a)? [K(r)-...

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...