Wyniki wyszukiwania

1

An extension of a theorem of Marcinkiewicz and Zygmund on differentiability

100%

Mukhopadhyay S. N., Mitra S.

Fundamenta Mathematicae

|

1996

|

tom 151

|

nr 1

21-38

EN

Let f be a measurable function such that $Δ_k(x,h;f) = O(|h|^λ)$ at each point x of a set E, where k is a positive integer, λ > 0 and $Δ_k(x,h;f)$ is the symmetric difference of f at x of order k. Marcinkiewicz and Zygmund [5] proved that if λ = k and if E is measurable then the Peano derivative $f_{(k)}$ exists a.e. on E. Here we prove that if λ > k-1 then the Peano derivative $f_{([λ])}$ exists a.e. on E and that the result is false if λ = k-1; it is further proved that if λ is any positive integer and if the approximate Peano derivative $f_{(λ),a}$ exists on E then $f_{(λ)}$ exists a.e. on E.

2

Intersection of sectorial cluster sets and directional essential cluster sets

80%

Layek A. K., Mukhopadhyay S. N.

Fundamenta Mathematicae

|

1980

|

tom 108

|

nr 2

99-107

3

Some properties of real functions of two variables and some consequences

79%

Mukhopadhyay S. N.

Fundamenta Mathematicae

|

1971-1972

|

tom 73

|

nr 3

249-259

4

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

On Dini derivatives and on certain classes of Zahorski

79%

Mukhopadhyay S. N.

Colloquium Mathematicum

|

1972

|

tom 25

|

nr 1

105-111

5

Symmetric derivative of nowhere monotone functions, I

70%

Kundu N. K., Mukhopadhyay S. N.

Annales Polonici Mathematici

|

1970

|

tom 23

|

nr 3

247-253

6

Relations between some general nth-order derivatives

70%

Bullen P. S., Mukhopadhyay S. N.

Fundamenta Mathematicae

|

1974

|

tom 85

|

nr 3

257-276

7

On functions of bounded n-th variation

60%

Mukhopadhyay S. N., Sain D. N.

Fundamenta Mathematicae

|

1988

|

tom 131

|

nr 3

191-208

8

On the approximate Peano derivatives

60%

Mukhopadhyay S. N.

Fundamenta Mathematicae

|

1975

|

tom 88

|

nr 2

133-143

9

On a certain property of the derivative

60%

Mukhopadhyay S. N.

Fundamenta Mathematicae

|

1970

|

tom 67

|

nr 3

279-284

10

On essential cluster sets

50%

Mukhopadhyay S. N.

Fundamenta Mathematicae

|

1973

|

tom 79

|

nr 2

159-171

11

On Schwarz differentiability, III

50%

Mukhopadhyay S. N.

Colloquium Mathematicum

|

1967

|

tom 17

|

nr 1

93-97

Ograniczanie wyników

8 Fundamenta Mathematicae

2 Colloquium Mathematicum

1 Annales Polonici Mathematici

11 Mukhopadhyay S. N.

1 Bullen P. S.

1 Kundu N. K.

1 Layek A. K.

1 Mitra S.

1 Sain D. N.

1 1996

1 1988

1 1980

1 1975

1 1974

1 1973

2 1972

2 1970

1 1967

An extension of a theorem of Marcinkiewicz and Zygmund on differentiability

Intersection of sectorial cluster sets and directional essential cluster sets

Some properties of real functions of two variables and some consequences

On Dini derivatives and on certain classes of Zahorski

Symmetric derivative of nowhere monotone functions, I

Relations between some general nth-order derivatives

On functions of bounded n-th variation

On the approximate Peano derivatives

On a certain property of the derivative

On essential cluster sets

On Schwarz differentiability, III