Note on the abstract generalized quasilinearization method


The abstract generalized quasilinearization method established in [2] for ordered Banach spaces with regular or normal cone and continuous mappings, is revisited for strongly minihedral cones and (o)-continuous operators


Adriana Buica
Babes-Bolyai University, Romania

Radu Precup
Babes-Bolyai University, Romania


Quasilinearization; ordered Banach space; cone; nonlinear operator equation; (o)-continuous operator; approximation

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A. Buica, R. Precup, Note on the abstract generalized quasilinearization method, Rev. Anal. Numer. Theor. Approx., 35 (2006) no. 1, 11-15.


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Revue d’analyse numérique et de théorie d’approximation

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Romanian Academy

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[1] Bellman, R. and Kalaba, R., Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965.
[2] Buica, A. and Precup, R., Abstract generalized quasilinearization method for coincidences, Nonlinear Stud., 9, pp. 371–387, 2002.
[3] Carl, S. and Heikkïa, S., Operator and differential equations in ordered spaces , J.Math. Anal. Appl., 234, pp. 31–54, 1999.
[4] Cristescu, R., Topological Vector Spaces, Editura Academiei Romane, Bucuresti and Noordhoff Int. Publ., Leyden, 1977.
[5] Deimling, K., Nonlinear Functional Analysis, Springer, Berlin, 1985.
[6] Lakshmikantham, V. and Vatsala, A. S., Generalized Quasilinearization for Nonlinear Problems, Kluwer, Dordrecht, 1998

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