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On the relationship between differentiability conditions and existence of a strong gradient. (English. Russian original) Zbl 1101.26012
Math. Notes 77, No. 1, 84-89 (2005); translation from Mat. Zametki 77, No. 1, 93-98 (2005).
This paper gives a negative answer to the question: Is differentiability almost equivalent to the existence of a strong gradient? Let us recall that the notion of a strong gradient was introduced by O. Dzagnidze [in: Collected papers in function theory. Proc. A. Razmadze Math. Inst. 106, 7–48 (1993; Zbl 0836.26007)].

MSC:
26B05 Continuity and differentiation questions
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[1] O. Dzagnidze, ”On the differentiability of functions of two variables and of an indefinite double integral,” Proc. A. Razmadze Math. Inst., 106 (1993), 7–48. · Zbl 0836.26007
[2] O. Dzagnidze, ”A necessary and sufficient condition for the differentiability of functions of several variables,” Proc. A. Razmadze Math. Inst., 123 (2000), 23–29. · Zbl 0971.26007
[3] S. Saks, Theory of the Integral, USA, 1939; Russian translation: Moscow, 1949.
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