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Journal of Inequalities and Applications
Published in: Journal of Inequalities and Applications 1/2006

Open Access 01-12-2006 | Research Article

Fuzzy multivalued variational inclusions in Banach spaces

Authors: S. S. Chang, D. O'Regan, J. K. Kim

Published in: Journal of Inequalities and Applications | Issue 1/2006

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Abstract

The purpose of this paper is to introduce the concept of general fuzzy multivalued variational inclusions and to study the existence problem and the iterative approximation problem for certain fuzzy multivalued variational inclusions in Banach spaces. Using the resolvent operator technique and a new analytic technique, some existence theorems and iterative approximation techniques are presented for these fuzzy multivalued variational inclusions.
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Literature
1.
Abbasbandy S, Viranloo TA, López-Pouso Ó, Nieto JJ: Numerical methods for fuzzy differential inclusions. Computers & Mathematics with Applications 2004,48(10–11):1633–1641. 10.1016/j.camwa.2004.03.009MathSciNetCrossRefMATH
2.
Agarwal RP, Khan MF, O'Regan D, Salahuddin : On generalized multivalued nonlinear variational-like inclusions with fuzzy mappings. Advances in Nonlinear Variational Inequalities 2005,8(1):41–55.MathSciNetMATH
3.
Agarwal RP, O'Regan D, Lakshmikantham V: Viability theory and fuzzy differential equations. Fuzzy Sets and Systems 2005,151(3):563–580. 10.1016/j.fss.2004.08.008MathSciNetCrossRefMATH
4.
Ammar EE, Hussein ML: Radiotherapy problem under fuzzy theoretic approach. Chaos, Solitons and Fractals 2003,18(4):739–744. 10.1016/S0960-0779(02)00682-3MathSciNetCrossRefMATH
5.
Aubin J-P: Mathematical Methods of Game and Economic Theory, Studies in Mathematics and Its Applications. Volume 7. North-Holland, Amsterdam; 1979:xxxii+619.
6.
Aubin J-P: Fuzzy differential inclusions. Problems of Control and Information Theory 1990,19(1):55–67.MathSciNetMATH
7.
Barbu V: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden; 1979.
8.
Chang SS: Variational Inequality and Complementarity Problems Theory and Applications. Shanghai Scientific and Technological Literature Publishing House, Shanghai; 1991.
9.
Chang SS: Some problems and results in the study of nonlinear analysis. Nonlinear Analysis. Theory, Methods & Applications 1997,30(7):4197–4208. 10.1016/S0362-546X(97)00388-XMathSciNetCrossRefMATH
10.
Chang SS: Set-valued variational inclusions in Banach spaces. Journal of Mathematical Analysis and Applications 2000,248(2):438–454. 10.1006/jmaa.2000.6919MathSciNetCrossRefMATH
11.
Chang SS: Existence and approximation of solutions for set-valued variational inclusions in Banach space. Nonlinear Analysis. Theory, Methods & Applications 2001,47(1):583–594. 10.1016/S0362-546X(01)00203-6MathSciNetCrossRefMATH
12.
Chang SS: Fuzzy quasivariational inclusions in Banach spaces. Applied Mathematics and Computation 2003,145(2–3):805–819. 10.1016/S0096-3003(03)00276-5MathSciNetCrossRefMATH
13.
Chang SS, Cho YJ, Lee BS, Jung IH: Generalized set-valued variational inclusions in Banach spaces. Journal of Mathematical Analysis and Applications 2000,246(2):409–422. 10.1006/jmaa.2000.6795MathSciNetCrossRefMATH
14.
Chang SS, Huang N-J: Generalized complementarity problems for fuzzy mappings. Fuzzy Sets and Systems 1993,55(2):227–234. 10.1016/0165-0114(93)90135-5MathSciNetCrossRefMATH
15.
Chang SS, Kim JK, Kim KH: On the existence and iterative approximation problems of solutions for set-valued variational inclusions in Banach spaces. Journal of Mathematical Analysis and Applications 2002,268(1):89–108. 10.1006/jmaa.2001.7800MathSciNetCrossRefMATH
16.
Chang SS, Zhu YG: On variational inequalities for fuzzy mappings. Fuzzy Sets and Systems 1989,32(3):359–367. 10.1016/0165-0114(89)90268-6MathSciNetCrossRefMATH
17.
Chidume CE, Zegeye H, Kazmi KR: Existence and convergence theorems for a class of multi-valued variational inclusions in Banach spaces. Nonlinear Analysis 2004,59(5):649–656.MathSciNetCrossRefMATH
18.
Ding XP: Generalized implicit quasivariational inclusions with fuzzy set-valued mappings. Computers & Mathematics with Applications 1999,38(1):71–79. 10.1016/S0898-1221(99)00170-4MathSciNetCrossRefMATH
19.
Ding XP, Park JY: A new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings. Journal of Computational and Applied Mathematics 2002,138(2):243–257. 10.1016/S0377-0427(01)00379-XMathSciNetCrossRefMATH
20.
Dubois D, Prade H: Fuzzy Sets and Systems. Theory and Applications, Mathematics in Science and Engineering. Volume 144. Academic Press, London; 1980:xvii+393.
21.
Feng G, Chen G: Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos, Solitons and Fractals 2005,23(2):459–467. 10.1016/j.chaos.2004.04.013MathSciNetCrossRefMATH
22.
Gu F: Iteration processes for approximating fixed points of operators of monotone type. Proceedings of the American Mathematical Society 2001,129(8):2293–2300. 10.1090/S0002-9939-00-05803-2MathSciNetCrossRefMATH
23.
Guo M, Xue X, Li R: Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets and Systems 2003,138(3):601–615. 10.1016/S0165-0114(02)00522-5MathSciNetCrossRefMATH
24.
Huang N-J, Cho YJ: Generalized strongly set-valued nonlinear complementarity problems. International Journal of Mathematics and Mathematical Sciences 1999,22(3):597–604. 10.1155/S0161171299225975MathSciNetCrossRefMATH
25.
Hüllermeier E: An approach to modelling and simulation of uncertain dynamical systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 1997,5(2):117–137. 10.1142/S0218488597000117MathSciNetCrossRefMATH
26.
27.
Lakshmikantham V, Mohapatra RN: Theory of Fuzzy Differential Equations and Inclusions, Series in Mathematical Analysis and Applications. Volume 6. Taylor & Francis, London; 2003:ix+178.MATH
28.
Lakshmikantham V, Nieto JJ: Differential equations in metric spaces: an introduction and an application to fuzzy differential equations. Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2003,10(6):991–1000.MathSciNetMATH
29.
Majumdar KK: One dimensional fuzzy differential inclusions. Journal of Intelligent & Fuzzy Systems 2003,13(1):1–5.CrossRefMATH
30.
31.
Nanda S, Pani S: Fuzzy variational inequality and complementarity problem. Journal of Fuzzy Mathematics 2004,12(1):231–235.MathSciNetMATH
32.
Nieto JJ, Torres A: Midpoints for fuzzy sets and their application in medicine. Artificial Intelligence in Medicine 2003,27(1):81–101. 10.1016/S0933-3657(02)00080-5CrossRef
33.
34.
Noor MA: Generalized set-valued variational inclusions and resolvent equations. Journal of Mathematical Analysis and Applications 1998,228(1):206–220. 10.1006/jmaa.1998.6127MathSciNetCrossRefMATH
35.
Noor MA: Variational inequalities for fuzzy mappings. II. Fuzzy Sets and Systems 1998,97(1):101–107. 10.1016/S0165-0114(96)00323-5MathSciNetCrossRefMATH
36.
Noor MA: Some algorithms for general monotone mixed variational inequalities. Mathematical and Computer Modelling 1999,29(7):1–9. 10.1016/S0895-7177(99)00058-8MathSciNetCrossRefMATH
37.
Noor MA: Set-valued quasi variational inclusions. The Korean Journal of Computational & Applied Mathematics 2000,7(1):101–113.MathSciNetMATH
38.
Noor MA: Variational inequalities for fuzzy mappings. III. Fuzzy Sets and Systems 2000,110(1):101–108. 10.1016/S0165-0114(98)00131-6MathSciNetCrossRefMATH
39.
Noor MA: Three-step approximation schemes for multivalued quasi variational inclusions. Nonlinear Functional Analysis and Applications 2001,6(3):383–394.MathSciNetMATH
40.
Noor MA: Multivalued quasi variational inclusions and implicit resolvent equations. Nonlinear Analysis. Theory, Methods & Applications 2002,48(2):159–174. 10.1016/S0362-546X(00)00177-2MathSciNetCrossRefMATH
41.
Noor MA: Two-step approximation schemes for multivalued quasi variational inclusions. Nonlinear Functional Analysis and Applications 2002,7(1):1–14.MathSciNetMATH
42.
O'Regan D, Lakshmikantham V, Nieto JJ: Initial and boundary value problems for fuzzy differential equations. Nonlinear Analysis 2003,54(3):405–415. 10.1016/S0362-546X(03)00097-XMathSciNetCrossRefMATH
43.
Park JY, Jeong JU: Generalized strongly quasivariational inequalities for fuzzy mappings. Fuzzy Sets and Systems 1998,99(1):115–120. 10.1016/S0165-0114(97)00027-4MathSciNetCrossRefMATH
44.
Park JY, Jeong JU: A perturbed algorithm of variational inclusions for fuzzy mappings. Fuzzy Sets and Systems 2000,115(3):419–424. 10.1016/S0165-0114(99)00116-5MathSciNetCrossRefMATH
45.
Salahuddin : An iterative scheme for a generalized quasivariational inequality. Advances in Nonlinear Variational Inequalities 2001,4(2):89–98.MathSciNetMATH
46.
Siddiqi AH, Ahmad R: An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces. International Journal of Mathematics and Mathematical Sciences 2004,2004(17–20):1035–1045.MathSciNetCrossRefMATH
47.
Uko LU: Strongly nonlinear generalized equations. Journal of Mathematical Analysis and Applications 1998,220(1):65–76. 10.1006/jmaa.1997.5796MathSciNetCrossRefMATH
48.
49.
Zeng L-C: Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities. Journal of Mathematical Analysis and Applications 1996,201(1):180–194. 10.1006/jmaa.1996.0249MathSciNetCrossRefMATH
50.
Zhu HY, Liu Z, Shim SH, Kang SM: Generalized multivalued quasivariational inclusions for fuzzy mappings. Advances in Nonlinear Variational Inequalities 2004,7(2):59–70.MathSciNetMATH
51.
Zimmermann HI: Fuzzy Set Theory and Its Applications. Kluwer Academic, Boston; 1965.
Metadata
Title
Fuzzy multivalued variational inclusions in Banach spaces
Authors
S. S. Chang
D. O'Regan
J. K. Kim
Publication date
01-12-2006
Publisher
Springer International Publishing
Published in
Journal of Inequalities and Applications / Issue 1/2006
Electronic ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/45164

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