Integral and differential test for convergence of operator series(in Ukrainian)

Author V. Yu. Slyusarchuk
V.Ye.Slyusarchuk@NUWM.rv.ua
Íàöiîíàëüíèé óíiâåðñèòåò âîäíîãî ãîñïîäàðñòâà òà ïðèðîäîêîðèñòóâàííÿ

Abstract We obtain the integral and differential conditions for convergence of operator series.
Keywords operator series; integral test; differential test
Reference 1. Slyusarchuk V.Yu. Conditions of converging operator series $\sum_{n=1}^\infty n^{-A}$// Nauk. Visnik of Chernivtsi University. – 2009. – V.485. – P. 113–117. (in Ukrainian)

2. Slyusarchuk V.Yu. Operator analogue of D’Alembert’s test// Mathematics today ’09. – Kiev: Izdat. “Osvita Ukraine”. – 2009. – V.15. – P. 101–115. (in Russian)

3. Slyusarchuk V.Yu. Operator analogue of Cauchy’s test// Mat. Stud. – 2010. – V.33, ¹1. – P. 97–100. (in Ukrainian)

4. Slyusarchuk V.Yu. Operator analogue of Bertrand’s test// Mat. Stud. – 2011. – V.35, ¹2. – P. 181–195. (in Ukrainian)

5. Slyusarchuk V.Yu. Operator analogue of Kummer’s test// Mat. Stud. – 2011. – V.36, ¹2. – P. 188–196. (in Ukrainian)

6. Fichtengolz G.M. Differential and integral calculus. – V.2, Moskow: Nauka, 1966, 800 p. (in Russian)

7. Slyusarchuk V.E. Some conditions for convergence of numerical series// Mathematics today ’90. – Kiev: Vishcha shkola. – 1990. – P. 94–105. (in Russian)

8. Slyusarchuk V.Yu. General theorems of converging numerical series. – Rivne: Rivne State Technical University Publishing House, 2001, 240 p. (in Ukrainian)

9. Krasnosel’skii M.A., Lifshic E.A., Sobolev A.V. Positive linear systems: method of positive operators. – Moskow: Nauka, 1985, 256 p. (in Russian)

Pages 178-189
Volume 39
Issue 2
Year 2013
Journal Matematychni Studii
Full text of paper PDF
Table of content of issue HTML