Eurasian Journal of Academic Research 4-jild 7-son (2024) · 1084–1086-betlar

ON SUMES OF ALMOST PERIODIC (A.P.) MULTI-VALUED FUNCTIONS

Nizomxonov, Erkinxon, Nizomxonov, Sanjarxon

DOI: 10.5281/zenodo.13364849 · Manbada o'qish →

Annotatsiya

This paper examines the basic properties of the sum of almost periodic multivalued functions whose values are compact sets of the space R^n. It is much more difficult to prove that the sum of two almost-periodic (a.p.) multi-valued functions is a multi- valued a.p. function. The first proof of this theorem for a single-valued function was given by G.Bohr. Subsequently, Bochner gave others a definition for unambiguous a.p. functions on which the almost-periodicity of the sum follows directly. Subsequently, it turned out that Bochner’s definition is very useful in many other questions of the theory of a.p. functions. Let us now give a definition for multi- valued a.p. functions, according to Bochner, and prove the equivalence of this definition with Bohr’s definition.

Almost periodic multivalued functions, spaces R^n, equivalence, arbitrary infinite sequence, real numbers, Sum of multivalued numbers

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