Note on the abstract generalized quasilinearization method
Keywords:quasilinearization, ordered Banach space, cone, nonlinear operator equation, (o)-continuous operator, approximation
AbstractThe abstract generalized quasilinearization method established in  for ordered Banach spaces with regular or normal cone and continuous mappings is revisited for strongly minihedral cones and (o)-continuous operators.
Bellman, R. and Kalaba, R., Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965.
Buică, A. and Precup, R., Abstract generalized quasilinearization method for coincidences, Nonlinear Stud., 9, pp. 371-387, 2002.
Carl, S. and Heikkilä, S., Operator and differential equations in ordered spaces, J. Math. Anal. Appl., 234, pp. 31-54, 1999, https://doi.org/10.1006/jmaa.1999.6299
Cristescu, R., Topological Vector Spaces, Editura Academiei Romane, Bucureşti and Noordhoff Int. Publ., Leyden, 1977.
Deimling, K., Nonlinear Functional Analysis, Springer, Berlin, 1985, https://doi.org/10.1007/978-3-662-00547-7
Lakshmikantham, V. and Vatsala, A. S., Generalized Quasilinearization for Nonlinear Problems, Kluwer, Dordrecht, 1998, https://doi.org/10.1007/978-1-4757-2874-3
How to Cite
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.