Progress in the open problems in theory of functions of bounded index

O. B. Skaskiv

doi:10.15330/ms.49.1.109-112

We give overview of solved problems in theory of functions of bounded index from the paper Bandura, A.I., Skaskiv, O.B.: Open problems for entire functions of bounded index in direction. Mat. Stud. 43(1), 103–109 (2015). Mostly problems concern with entire functions of several variables and analytic theory of differential equations. We pose also new problems.

1. Bandura A., Skaskiv O., Entire functions of bounded L-index: Its zeros and behavior of partial logarithmic derivatives, J. Complex Analysis, 2017 (2017), 1–10.

2. Bandura A.I., Skaskiv O.B., Analytic functions in the unit ball of bounded L-index: asymptotic and local properties, Mat. Stud., 48 (2017) №1, 37–73.

3. Bandura A., Skaskiv O., Asymptotic estimates of entire functions of bounded L-index in joint variables Novi Sad J. Math., 48 (2018) №1, 103–116.

4. Bandura A.I., Skaskiv O.B., Growth of entire functions of bounded L-index in direction, Mat. Met. Phys.-mech. fields, 60 (2017) №1, 22–31.

5. Bandura A.I., Skaskiv O.B., Sufficient sets for boundedness L-index in direction for entire functions, Mat. Stud., 30 (2008), №2, 177–182.

6. Bandura A.I., A class of entire functions of unbounded index in each direction, Mat. Stud., 44 (2015), №1, 107–112.

7. Bandura A.I., Some improvements of criteria of L-index boundedness in direction, Mat. Stud., 47 (2017), №1, 27–32.

8. Bandura A., Skaskiv O., Filevych P., Properties of entire solutions of some linear PDE’s, J. Appl. Math. Comput. Mech., 16 (2017), №2, 17–28.

9. Bandura A., Composition of entire functions and bounded L-index in direction, Mat. Stud., 47 (2017), №2, 179–184.

10. Bandura A.I., Skaskiv O.B., Open problems for entire functions of bounded index in direction, Mat. Stud., 43 (2015) №1, 103–109.

11. Bandura A.I., Skaskiv O.B., Directional logarithmic derivative and the distribution of zeros of an entire function of bounded L-index along the direction, Ukrain. Mat. J., 69 (2017), №3, 500–508.

12. Bandura A., Skaskiv O., Entire functions of several variables of bounded index, Lviv: Publisher I.E. Chyzhykov, 2016, 128 p.

13. Goldberg A.A., On the growth of entire solutions of algebraic differential equations, Lithuanian Mathematical Journal, 45 (2005) №1, 44–49.

14. Hayman W.K., Differential inequalities and local valency, Pacific J. Math., 44 (1973) №1, 117–137.

	Progress in the open problems in theory of functions of bounded index
Author	O. B. Skaskiv olskask@gmail.com Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract	We give overview of solved problems in theory of functions of bounded index from the paper Bandura, A.I., Skaskiv, O.B.: Open problems for entire functions of bounded index in direction. Mat. Stud. 43(1), 103–109 (2015). Mostly problems concern with entire functions of several variables and analytic theory of differential equations. We pose also new problems.
Keywords	bounded L-index in direction; entire function; several variables; bounded L-index in joint variables
DOI	doi:10.15330/ms.49.1.109-112
Reference	1. Bandura A., Skaskiv O., Entire functions of bounded L-index: Its zeros and behavior of partial logarithmic derivatives, J. Complex Analysis, 2017 (2017), 1–10. 2. Bandura A.I., Skaskiv O.B., Analytic functions in the unit ball of bounded L-index: asymptotic and local properties, Mat. Stud., 48 (2017) №1, 37–73. 3. Bandura A., Skaskiv O., Asymptotic estimates of entire functions of bounded L-index in joint variables Novi Sad J. Math., 48 (2018) №1, 103–116. 4. Bandura A.I., Skaskiv O.B., Growth of entire functions of bounded L-index in direction, Mat. Met. Phys.-mech. fields, 60 (2017) №1, 22–31. 5. Bandura A.I., Skaskiv O.B., Sufficient sets for boundedness L-index in direction for entire functions, Mat. Stud., 30 (2008), №2, 177–182. 6. Bandura A.I., A class of entire functions of unbounded index in each direction, Mat. Stud., 44 (2015), №1, 107–112. 7. Bandura A.I., Some improvements of criteria of L-index boundedness in direction, Mat. Stud., 47 (2017), №1, 27–32. 8. Bandura A., Skaskiv O., Filevych P., Properties of entire solutions of some linear PDE’s, J. Appl. Math. Comput. Mech., 16 (2017), №2, 17–28. 9. Bandura A., Composition of entire functions and bounded L-index in direction, Mat. Stud., 47 (2017), №2, 179–184. 10. Bandura A.I., Skaskiv O.B., Open problems for entire functions of bounded index in direction, Mat. Stud., 43 (2015) №1, 103–109. 11. Bandura A.I., Skaskiv O.B., Directional logarithmic derivative and the distribution of zeros of an entire function of bounded L-index along the direction, Ukrain. Mat. J., 69 (2017), №3, 500–508. 12. Bandura A., Skaskiv O., Entire functions of several variables of bounded index, Lviv: Publisher I.E. Chyzhykov, 2016, 128 p. 13. Goldberg A.A., On the growth of entire solutions of algebraic differential equations, Lithuanian Mathematical Journal, 45 (2005) №1, 44–49. 14. Hayman W.K., Differential inequalities and local valency, Pacific J. Math., 44 (1973) №1, 117–137.
Pages	109-112
Volume	49
Issue	1
Year	2018
Journal	Matematychni Studii
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