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On the existence of fixed points in completely continuous operators in F-space

Annotation

This work is dedicated to the development of the theory of fixed points of completely continuous operators. We prove existence of new theorems of fixed points of completely continuous operators in F -space (Frechet space). This class of spaces except Banach includes such important space as a countably normed space and Lp(0<p<1); lp(0<p<1).

Keywords

banach space; F-space; completely continuous operator; fixed point

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DOI

10.20310/1810-0198-2019-24-125-26-32

UDC

517.988

Pages

26-32

References

[1] M. A. Krasnoselskii, Positive Solutions of Operator Equations, Fizmatgiz, Moscow, 1962 (In Russian). [2] M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostekhizdat, Moscow, 1956 (In Russian). [3] I. A. Bakhtin, Positive Solutions of Nonlinear Equations with Concave Operators, a manual for special course, Voronezh State Pedagogical Institute, Voronezh, 1985 (In Russian). [4] I. A. Bakhtin, Nonlinear Equations with Monotone Operators, a manual for special course, Voronezh State Pedagogical Institute, Voronezh, 1988 (In Russian). [5] A. N. Dorokhov, “The fixed points of completely continuous operators in F -space”, News of the Voronezh State Pedagogical University, 257 (2011), 8–15 (In Russian). [6] K. Yoshida, Functional Analysis, World, Moscow, 1967 (In Russian). [7] L. V. Kantorovich, G.P. Akilov, Functional Analysis, Science, Moscow, 1977 (In Russian).

Section of issue

Scientific articles

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