On one question of analysis
Authors:
Abstract
К. Begl formulates the definitions of continuity and directional derivative in the space Rn in such a way that they respectively have a unified general form for all n and coincide at n=1 with the corresponding definitions for functions of one variable. In addition to the concept of continuity, the concepts of derivative, integral, convergence, semicontinuity, and limit, expressed in a unified and general form, are introduced successively.
Funding:
None
References
- Bogel K. J. reine und angew. Math., 1934, vol. 170, p. 197; 1935, vol. 173, p. 5.
- Nicolescu M. Bull. Math. București, 1941.
- Dobrescu E. Studii si cercetari mat. Acad. RPR, 1957, No. 1–2.
- Salagean I. Comun. Acad. RPR, 1960, No. 11.
- Dobrescu E. Comun. Acad. RPR, 1960, No. 10.
- Blumberg H. Trans. Amer. Math. Soc., 1919, vol. 20, No. 1.
- Valiron G. Proc. Phys. Soc. Japan, 1931, No. 19.
- Montel P. J. Math. pures et appl., 1928, vol. VII.
- Montel P. Praktika de l'Acad. d'Athènes, 1931, No. 6.
- Nicolescu M. Analiza matematica, 1959, No. 11.
- Dobrescu E., Salagean I. Comun. Acad. RPR, 1959, v. IX, No. 3, 5.