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
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
| № | Muallifning F.I.Sh. | Lavozimi | Tashkilot nomi |
|---|---|---|---|
| 1 | Nizomxonov S.E. | ! | University of Tashkent for Applied Sciences, |
| 2 | Nizomxonov E.N. | ! | University of Tashkent for Applied Sciences, |
| № | Havola nomi |
|---|---|
| 1 | [1].Gulyamov, S.S. va b. (2019). Raqamli iqtisodiyotda Levitan B.M. Almost periodic functions. –M.: GITTL, 1953. –396 p.[2].Levitan B.M., Zhikov V.V. Almost periodic functions and differential equations. –M.: Publishing house. Moscow State University. 1978.[3].Banzaru T. Aplicatii multi voce aproape-periodioe, Bul.Sti.Pehnic Inat. Polytechnic Fimisoava . Mat. fiz.-mec .19(33). fabc , 1 (1974), p 25–26.[4].Banzaru T., Cvivat N. Asupva applicate multi voce apvoape-periodice cu voloviin spatii uniforme. Bul. Sti Pehnis Inst. Polytechnic Fimisoava, Mat.-fiz., 1981, 26 (40) fasc (2) p.47–51.[5].Borisovich Yu.G., Gelmant B.D., Mashkis A.D., Obukhovsky V.V. “Introduction to the theory of multivalued mappings” Voronezh. VSU Publishing House,1986.[6].Povolotsky A.I., Nizomkhanov E. On almost periodic multivalued functions. -Ulyanov. Ed., UGU, 1986. –P.90 –97.[1]Demidovich B.P. Lectures on the mathematical theory of stability. –M.: Nauka, 1967. –472 p. |