Hostname: page-component-cc8bf7c57-5wl6q Total loading time: 0 Render date: 2024-12-12T02:03:42.529Z Has data issue: false hasContentIssue false

On generalised mixed co-quasi-variational inequalities with noncompact valued mappings

Published online by Cambridge University Press:  17 April 2009

Rais Ahmad
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India, e-mail: [email protected]
Qamrul Hasan Ansari
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, P.O. Box 1169, Dhahran 31261, Saudi Arabiaa, e-mail: [email protected] Second author is on leave from Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India, e-mail: [email protected]
Syed Shakaib Irfan
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we consider generalised mixed co-quasi-variational inequalities with noncompact valued mappings and propose an iterative algorithm for computing their approximate solutions. We prove that the approximate solutions obtained by the proposed algorithm converge to the exact solution of our co-quasi-variational inequality. Some special cases are also discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Alber, Y., ‘Metric and generalized projection operators in Banach Spaces; properties and applications’, in Theory and Applications of Nonlinear Opεrators of Monotone and Accretive Type, (Kartsatos, A., Editor) (Marcel Dekker, New York, 1996), pp. 1550.Google Scholar
[2]Alber, Y. and Yao, J.C., ‘Algorithm for generalized multi-valued co-variational inequalities in Banach Spaces’, Funct. Differ. Equ. 7 (2000), 513.Google Scholar
[3]Banyamini, Y. and Lindenstrauss, J., Geometric nonlinear functional analysis, I, American Mathematical Society Colloquium Publications 48 (American Mathematical Society, Providence, R.I., 2000).Google Scholar
[4]Chang, S.S., ‘On the Mann and Ishikawa iterative approximation of solution to variational inclusions with accretive mappings’, Comput. Math. Appl. 37 (1999), 1724.CrossRefGoogle Scholar
[5]Chipot, M., Elements of nonlinear analysis (Birkhauser Verlag, Berlin, 2000).CrossRefGoogle Scholar
[6]Glowinski, R., Lions, J.L. and Tremolieres, R., Numerical analysis of variational inequalities (North-Holland, Amsterdam, 1981).Google Scholar
[7]Goebel, K. and Reich, S., Uniform convexity, hyperbolic geometry and nonexpansive mappings (Marcel Dekker, New York, N.Y., 1984).Google Scholar
[8]Guo, J.S. and Yao, J.C., ‘Extension of strongly nonlinear quasivariational inequalities’, Appl. Math. Lett. 5 (1992), 3538.CrossRefGoogle Scholar
[9]Isac, G., Complementarity problems (Springer-Verlag, Berlin, 1992).Google Scholar
[10]Isac, G., Topological methods in complementarity theory (Kluwer Academic Publishers, Dordrecht, Boston, London, 2000).Google Scholar
[11]Kinderlehrer, D. and Stampacchia, G., An introduction to variational inequalities and their applications (Academic Press, New York, 1980).Google Scholar
[12]Nadler, S.B. Jr, ‘Multi-valued contraction mappings’, Pacific J. Math. 30 (1969), 475488.CrossRefGoogle Scholar
[13]Siddiqi, A.H. and Ansari, Q.H., ‘Strongly nonlinear quasivariational inequalities’, J. Math. Anal. Appl. 149 (1990), 444450.Google Scholar
[14]Siddiqi, A.H. and Ansari, Q.H., ‘General strongly nonlinear variational inequalities’, J. Math. Anal. Appl. 166 (1992), 386392.Google Scholar
[15]Takahashi, W. and Kim, G.-E., ‘Strong convergence of approximates to fixed points of nonexpansive nonself-mappings in Banach spaces’, Nonlinear Anal. 32 (1998), 447454.Google Scholar
[16]Verma, R.U., ‘On generalized variational inequalities involing relaxed Lipschitz and relaxed monotone operators’, J. Math. Anal. Appl. 213 (1997), 387392.CrossRefGoogle Scholar
[17]Yao, J.C., ‘Applications of variational inequalities to nonlinear analysis’, Appl. Math. Lett. 4 (1991), 8992.Google Scholar