Menu: Home :: go to Journal :: switch to Russian :: switch to English
You are here: all Journals and Issues→ Journal→ Issue→ Article

ON QUADRATIC MAPPINGS PROPERTIES AND CONDITIONS FOR INVERSE FUNCTIONS EXISTENCE

Annotation

Some properties of quadratic mappings are studied It is proved that if a quadratic mapping have no nontrivial zeroes then it has nontrivial fixed points. Sufficient conditions for inverse function existence are obtained for smooth mappings in the case when the first derivative vanishes.

Keywords

quadratic mapping; fixed point; inverse function

Full-text in one file

Download

DOI

10.20310/1810-0198-2017-22-3-533-538

UDC

517.275

Pages

533-538

References

1. Arutyunov A.V. Smooth abnormal problems in extremum theory and analysis // Russian Mathematical Surveys. 2012. V. 67. Iss. 3. P. 403–457. 2. Arutyunov A.V., Magaril-Ilyayev G.G., Tikhomirov V.M. Pontryagin’s maximum principle. Moscow, Factorial-Press, 2006. 3. Avakov E.R., Arutyunov A.V. Inverse function theorem and conditions of extremum for abnormal problems with non-closed range // Sb. Math. 2005. V. 196. Iss. 9. P. 1251–1269. 4. Milnor J.W., Wallace A.H. Differential Topology. Basic course. Moscow, Mir, 1972. 5. Krasnosel’skii M.A. Topological Methods in the Theory of Nonlinear Integral Equations, Mosocow, Gosudarstvennoe izdatel’stvo tekniko-teoreticheskoy literaturi, 1956.

Received

2017-04-20

Section of issue

Functional-differential equations and inclusions and their applications to mathematical modeling

Для корректной работы сайта используйте один из современных браузеров. Например, Firefox 55, Chrome 60 или более новые.