Quasilinearity of Some Composite Functionals with Applications (original) (raw)

A Characterization of Convex and Semicoercive Functionals

2001

In this paper we prove that every proper convex and lower semicontinuous functional Φ defined on a real reflexive Banach space X is semicoercive if and only if every small uniform perturbation of Φ attains its minimum value on X.

Biquasilinear Functionals on Quasilinear Spaces and Some Related Results

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2020

In this paper, we will present the notion of the biquasilinear functional which is a new concept of quasilinear functional analysis. Just like bilinear functional, the notions of a biquasilinear functional and a quadratic form will not need to have the constitution of an inner product quasilinear space. We were able to define these functionals in any quasilinear space. After giving this new notion, we discuss some examples and prove some theorems for considerable exercises to the theory of biquasilinear functionals in Hilbert quasilinear spaces.

On the Jensen Functional and Strong Convexity

Bulletin of the Malaysian Mathematical Sciences Society, 2016

In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concept of a strongly convex function.

Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions

Nonlinear Analysis: Theory, Methods & Applications, 2010

The principal aim of this paper is to show that weakly cone-convex vector-valued functions, as well as weakly cone-quasiconvex vector-valued functions, can be characterized in terms of usual weakly convexity and weakly quasiconvexity of certain real-valued functions, defined by means of the extreme directions of the polar cone or by Gerstewitz's scalarization functions.

Integrals which are convex functionals

Pacific Journal of Mathematics, 1968

This paper examines numerical functionals defined on function spaces by means of integrals having certain convexity properties. The functionals are themselves convex, so they can be analysed in the light of the theory of conjugate convex functions, which has recently undergone extensive development. The results obtained are applicable to Orlicz space theory and in the study of various extremum problems in control theory and the calculus of variations.

Subdifferential Characterization of Quasiconvexity and Convexity

Journal of Convex Analysis, 1994

Let f: X! IR f+1g be a lower semicontinuous function on a Banach space X. We show that f is quasiconvex if and only if its Clarke subdi erential@ f is quasimonotone. As an immediate consequence, we get that f is convex if and only if@ f is monotone.

Dominated extensions of functionals and V-convex functions of cancellative cones

Bulletin of the Australian Mathematical Society, 2003

Let C be a cancellative cone and consider a subcone Co of C. We study the natural problem of obtaining conditions on a non negative homogeneous function : C-> R + so that for each linear functional / defined in Co which is bounded by , there exists a linear extension to C In order to do this we assume several geometric conditions for cones related to the existence of special algebraic basis of the linear span of these cones.