Volume 3,  Issue 2, 2002

Article 28

TWO REMARKS ON THE STABILITY OF GENERALIZED HEMIVARIATIONAL INEQUALITIES

MOHAMED AIT MANSOUR

CADI AYYAD UNIVESITY
SEMLALIA FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS,
B.P. 2390, 40 000-MARRAKESH,
MOROCCO
E-Mail: mansour@ucam.ac.ma
URL: http://www.angelfire.com/nb/mansour/

Received 5 March, 2001; Accepted 30 January, 2002.
Communicated by: Z. Nashed

ABSTRACT.   The present paper is devoted to the stability analysis of a general class of hemivariational inequalities. Essentially, we present two approaches for this class of problems. First, using a general version of Minty's Lemma and the convergence result of generalized gradients due to T. Zolezzi [23], we prove a stability result in the spirit of Mosco's results on the
variational inequalities [14]. Second, we provide a quite different stability result with an estimate for the rate of convergence of solutions when the given perturbed data are converging with respect to an appropriate distance. Illustration is given with respect to a hemivariational inequality modelling the buckling of adhesively connected von kārmān plates.

[14] U. MOSCO, Convergence of Convex Sets and of Solutions of Variational Inequalities.
[23] T. Zolezzi, Convergence of Generalized Gradients.

Key words:
Generalized hemivariational inequalities, Clarke's gradient, Perturbation, Epi-convergence, Stability, Rate of convergence, Equilibrium problems, von kārmān plates.

2000 Mathematics Subject Classification:
49J40, 40J45, 49J52.

Download this article (PDF):

Suitable for a printer:    

Suitable for a monitor:        

 To view these files we recommend you save them to your file system and then view by using the Adobe Acrobat Reader. 

That is, click on the icon using the 2nd mouse button and select "Save Target As..." (Microsoft Internet Explorer) or "Save Link As..." (Netscape Navigator).

See our PDF pages for more information.
 

Other papers in this issue

An Error Estimate for Finite Volume Methods for the Stokes Equations
A. Alami-Idrissi and M. Atounti 

On Some Retarded Integral Inequalities and Applications 
B.G. Pachpatte 

Littlewood's Inequality for p-Bimeasures
Nasser Towghi

Monotonicity Properties of the Relative Error of a Padé Approximation for Mills' Ratio
Iosif Pinelis 

Integral Inequalities of the Ostrowski Type
A.Sofo

Multidimensional Extension of L.C. Young's Inequality
Nasser Towghi 

Inequalities for Lattice Constrained Planar Convex Sets
 Poh Wah Hillock and Paul R. Scott 

Some Results Concerning Best Uniform Coapproximation
Geetha S. Rao and R. Saravanan

Strongly Elliptic Operators for a Plane Wave Diffraction Problem in Bessel Potential Spaces
L.P. Castro

Some Integral Inequalities Involving Taylor's Remainder. I
Hillel Gauchman

On Multidimensional Grüss Type Inequalities
Baburao G. Pachpatte

Two Remarks on the Stability of Generalized Hemivariational Inequalities
 Mohamed Ait Mansour 

Note on the Perturbed Trapezoid Inequality
 Xiao-liang Cheng and Jie Sun

On a Noncoercive System of Quasi-Variational Inequalities Related to Stochastic Control Problems
M. Boulbrachene, M. Haiour and B. Chentouf

An Inequality Improving the First Hermite-Hadamard Inequality for Convex Functions Defined on Linear Spaces and Applications for Semi-Inner Products
 S.S. Dragomir

 

Other issues
 

Š 2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.

Copyright/Disclaimer