zbMATH — the first resource for mathematics

The role of matrices that are convergent to zero in the study of semilinear operator systems. (English) Zbl 1165.65336
Summary: We explain the advantage of vector-valued norms and the role of matrices that are convergent to zero in the study of semilinear operator systems by means of some basic methods of nonlinear analysis: the contraction principle, Schauder’s fixed point theorem, the Leray-Schauder continuation principle and Krasnoselskii’s cone fixed point theorem. A vector version of Krasnoselskii’s theorem is also established.

65F30 Other matrix algorithms (MSC2010)
47J25 Iterative procedures involving nonlinear operators
15A99 Basic linear algebra
47H10 Fixed-point theorems
Full Text: DOI
[1] Avramescu, C., Sur l’existence des solutions convergentes pour des équations intégrales, An. univ. craiova ser. V, 2, 87-98, (1974) · Zbl 0306.45015
[2] Granas, A.; Dugundji, J., Fixed point theory, (2003), Springer New York · Zbl 1025.47002
[3] Jensen, B.S., The dynamic systems of basic economic growth models, (1994), Kluwer Dordrecht · Zbl 0829.90027
[4] Murray, J.D., Mathematical biology, (1989), Springer Berlin · Zbl 0682.92001
[5] D. Muzsi, R. Precup, Nonresonance and existence for systems of semilinear operator equations (in press) · Zbl 1169.47053
[6] O’Regan, D.; Precup, R., Theorems of leray – schauder type and applications, (2001), Gordon and Breach Amsterdam · Zbl 1045.47002
[7] Perov, A.I.; Kibenko, A.V., O a certain general method for investigation of boundary value problems, Izv. akad. nauk SSSR, 30, 249-264, (1966), (in Russian)
[8] Precup, R., Methods in nonlinear integral equations, (2002), Kluwer Dordrecht · Zbl 1060.65136
[9] I.A. Rus, Principles and Applications of the Fixed Point Theory (Romanian), Dacia, Cluj, 1979
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.