On the stability of the linear mapping in Banach spaces

Proceedings of the American Mathematical Society - Tập 72 Số 2 - Trang 297-300
Themistocles M. Rassias1
1Department of Mathematics of the University of California at Berkeley.

Tóm tắt

Let E 1 , E 2 {E_1},{E_2} be two Banach spaces, and let f : E 1 → E 2 f:{E_1} \to {E_2} be a mapping, that is “approximately linear". S. M. Ulam posed the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist". The purpose of this paper is to give an answer to Ulam’s problem.

Từ khóa


Tài liệu tham khảo

Hyers, D. H., 1941, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27, 222, 10.1073/pnas.27.4.222

T. M. Rassias, Vector fields on Banach manifolds (to appear).

Rudin, Walter, 1962, Fourier analysis on groups

Ulam, S. M., 1964, Problems in modern mathematics

Ulam, Stanislaw, 1974, Sets, numbers, and universes: selected works

K. Yosida, Functional analysis, Springer, Berlin-Göttingen-Heidelberg, 1965.

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Thông tin xuất bản

Proceedings of the American Mathematical Society

Tập 72 Số 2

297-300

Thông tin tác giả