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Volume 1, Issue 2, 2000

Article 15

http://jipam.vu.edu.au/v1n2/015_99.html

ON THE GENERALISED STRONGLY NONLINEAR IMPLICIT QUASIVARIATIONAL INEQUALITIES FOR STE-VALUED MAPPINGS

1 YEOL JE CHO, 2 ZHI HE, 2 YUN FEI CAO 
AND 2 NAN JING HUANG

1DEPARTMENT OF MATHEMATICS,
GYEONGSANG NATIONAL UNIVERSITY,
CHINJU 660-701, KOREA
E-Mail: yjcho@nongae.gsnu.ac.kr

2DEPARTMENT OF  MATHEMATICS,
 SICHUAN UNIVERSITY, 
CHENGDU, SICHUAN 610064, 
PEOPLE'S REPUBLIC OF CHINA

Received 22 November, 1999; accepted 12 April, 2000.
Communicated by: S.S. Dragomir.

ABSTRACT. In this paper, we introduce and study a new class of generalized strongly nonlinear implicit quasivariational inequalities for set-valued mappings and construct some new iterative algorithms for this kind of generalized strongly nonlinear implicit quasivariational inequalities by using the projection method and Nadler's theorem. We prove some existence theorems of solutions for this kind of generalized nonlinear strongly implicit quasivariational inequalities for set-valued mappings without compactness and convergence theorems of iterative sequences generated by the algorithms.
Key words:
Nonlinear implicit quasivariational inequality, set-valued mapping, projection algorithm, Hausdorff metric, Hilbert space.

2000 Mathematics Subject Classification: 49J40, 47H06.
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Other papers in this issue

Ostrowski type inequalities from a linear functional point of view
I. Gavrea and B. Gavrea

A Grüss type inequality for sequences of vectors in inner product spaces and applications
 S.S. Dragomir

On an Bojanic-Stanojevic type inequality
 Z. Tomovski

Regularity results for vector fields of bounded distortion and applications
 A. Fiorenza and F. Giannetti

Inequalities for power-exponential functions
 F. Qi and L. Debnath

On the generalized strongly nonlinear implicit quasivariational inequalities for set-valued mappings
 Y.J. Cho, Z. He, Y. F. Cao and N. J. Huan

A new look at Newton's inequalities
 C. P. Niculescu

An application of almost increasing and d-quasi monotone sequences
 H. Bor

Several integral inequalities
 F. Qi

On integral inequalities of Gronwall-Bellman-Bihari type in several variables
 J. A. Oguntuase

Some inequalities for the expectation and variance of a random variable whose PDF is n-time differentiable
N.S. Barnett, P. Cerone, S.S. Dragomir and J. Roumeliotis

On a Strengthened Hardy-Hilbert Inequality
B. Yang

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© 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.

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