Note on the abstract generalized quasilinearization method

Authors

  • Adriana Buică
  • Radu Precup "Babeş Bolyai" University, Cluj-Napoca, Romania

Keywords:

quasilinearization, ordered Banach space, cone, nonlinear operator equation, (o)-continuous operator, approximation

Abstract

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.

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References

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

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Published

2006-02-01

How to Cite

Buică, A., & Precup, R. (2006). Note on the abstract generalized quasilinearization method. Rev. Anal. Numér. Théor. Approx., 35(1), 11–15. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no1-art3

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