Abstract
In the current work, we introduce and study completely generalized co-complementarity problems for fuzzy mappings (for short, CGCCPFM). By using the definitions of p-relaxed accretive and p-strongly accretive mappings, we propose an iterative algorithm for computing the approximate solutions of CGCCPFM. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of CGCCPFM.
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References
R. Ahmad, S. S. Irfan, Generalized quasi-complementarity problems with fuzzy set-valued mappings. International J. Fuzzy System. 5(3), 194–199 (2003)
Ya Alber, Metric and Generalized Projection Operators in Banach Spaces, Properties and Applications, in Theory and Applications of Nonlinear Operators of Monotone and Accretive Type, ed. by A. Kartsatos (Marcel Dekker, New York, 1996), p. 15–50
Q. H. Ansari, A. P. Farajzadeh, S. Schaible, Existence of solutions of vector variational inequalities and vector complementarity Problems. J. Glob. Optim. [45 (2), 297–307 (2009)]
F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces. Bull. Amer. Math. Soc. 73, 875–885 (1967)
R. W. Cottle, Nonlinear programs with positively bounded Jacobians. SIAM J. Appl. Math. 14, 125–147 (1966)
R. W. Cottle, G. B. Dantzing, Complementarity pivot theory of mathematical programming. Linear Algebra Appl. 1, 163–185 (1968)
M. F. Khan, Salahuddin, Generalized co-complementarity problems in p-uniformly smooth Banach spaces. J. Inequal. Pure and Appl. Math. 7(2) 66, 1–11 (2006)
S. J. Habetler, A. L. Price, Existence theory for generalized nonlinear complementarity problems. J. Optim. Theo. Appl. 7, 223–239 (1971)
G. Isac, On the implicit complementarity problem in Hilbert spaces. Bull. Austral. Math. Soc. 32, 251–260 (1985)
G. Isac, Fixed point theory and complementarity problem in Hilbert spaces. Bull. Austral. Math. Soc. 36, 295–310 (1987)
C. R. Jou, J. C. Yao, Algorithm for generalized multivalued variational inequalities in Hilbert spaces. Comput. Math. Appl. 25(9), 7–13 (1993)
S. Karmardian, Generalized complementarity problems. J. Optim. Theo. Appl. 8, 161–168 (1971)
T. Kato, Nonlinear semigroups and evolution equations. J. Math. Soc. Japan. 18/19, 508–520 (1967)
S. B. Nadler, Jr., Multivalued contraction mappings. Pacific J. Math. 30, 475–488 (1969)
M. A. Noor, Nonlinear quasi-complementarity problems. Appl. Math. Lett. 2(3), 251–254 (1980)
M. A. Noor, On nonlinear complementarity problems. J. Math. Anal. Appl. 123, 455–460 (1987)
A. H. Siddiqi, Q. H. Ansari, On the nonlinear implicit complementarity problem. Int. J. Math. and Math. Sci. 16(4), 783–790 (1993)
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Dedicated to the memory of Professor George Isac
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Siddiqi, A.H., Irfan, S.S. (2010). Completely Generalized Co-complementarity Problems Involving p-Relaxed Accretive Operators with Fuzzy Mappings. In: Pardalos, P., Rassias, T., Khan, A. (eds) Nonlinear Analysis and Variational Problems. Springer Optimization and Its Applications, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0158-3_28
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DOI: https://doi.org/10.1007/978-1-4419-0158-3_28
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