Note on the abstract generalized quasilinearization method

Authors

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

DOI:

https://doi.org/10.33993/jnaat351-1006

Keywords:

quasilinearization, ordered Banach space, cone, nonlinear operator equation, (o)-continuous operator, approximation
Abstract views: 191

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. DOI: https://doi.org/10.1109/TAC.1965.1098135

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 DOI: 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 DOI: 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 DOI: 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. https://doi.org/10.33993/jnaat351-1006

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