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General method of regularization. II: Relaxation proposed by suquet

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

Mohammad Chowdhury, Kok-Keong Tan (2010)

Open Mathematics

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s...

Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces

R. W. Hansell, L. Oncina (2005)

Czechoslovak Mathematical Journal

In this paper we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

Chowdhury, Mohammad (1998)

Serdica Mathematical Journal

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.Existence theorems of generalized variational inequalities and generalized complementarity problems are obtained in topological vector spaces for demi operators which are upper hemicontinuous along line segments in a convex set X. Fixed point theorems are also given in Hilbert spaces for set-valued operators T which are upper hemicontinuous along line segments in X such...

Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

Bapurao Chandra Dhage (2007)

Archivum Mathematicum

In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage (Dhage, B. C., A fixed...

Implicit integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1997)

Commentationes Mathematicae Universitatis Carolinae

We consider the integral equation h ( u ( t ) ) = f ( ∫ I g ( t , x ) u ( x ) d x ) , with t ∈ [ 0 , 1 ] , and prove an existence theorem for bounded solutions where f is not assumed to be continuous.

Lectures on maximal monotone operators.

R. R. Phelps (1997)

Extracta Mathematicae

These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces.

Local analysis of a cubically convergent method for variational inclusions

Steeve Burnet, Alain Pietrus (2011)

Applicationes Mathematicae

This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from ℝ q to the closed subsets of ℝ q . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.

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