Wyniki wyszukiwania

1

An inconsistency equation involving means

100%

Ger R., Kochanek T.

Colloquium Mathematicum

|

2009

|

tom 115

|

nr 1

87-99

EN

We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations $f(M(x,y)) = A_{φ}(f(x),f(y))$ and $f(A_{φ}(x,y)) = M(f(x),f(y))$ are the constant ones.

2

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Mean values for vector valued functions and corresponding functional equations

100%

Ger R., Sablik M.

Commentationes Mathematicae

|

2013

|

tom 53

|

nr 2

EN

Although, in general, a straightforward generalization of the Lagrange mean value theorem for vector valued mappings fails to hold we will look for what can be salvaged in that situation. In particular, we deal with Sanderson's and McLeod's type results of that kind (see [9] and [7], respectively). Moreover, we examine mappings with a prescribed intermediate point in the spirit of the celebrated Acz\'el's theorem characterizing polynomials of degree at most 2 (cf. [1]).

3

Errata list for "Mean values for vector valued functions and corresponding functional equations" (Commentationes Mathematicae 53(2) (2013), 355-369)

100%

Ger R., Sablik M.

Commentationes Mathematicae

|

2014

|

tom 54

|

nr 1

4

On two functional equations connected with distributivity of fuzzy implications

81%

Ger R., Kuczma M. E., Niemyska W.

Commentationes Mathematicae

|

2015

|

tom 55

|

nr 2

EN

The distributivity law for a fuzzy implication $I\colon [0,1]^2 \to [0,1]$ with respect to a fuzzy disjunction $S\colon [0,1]^2 \to [0,1]$ states that the functional equation $ I(x,S(y,z))=S(I(x,y),I(x,z)) $ is satisfied for all pairs $(x,y)$ from the unit square. To compare some results obtained while solving this equation in various classes of fuzzy implications, Wanda Niemyska has reduced the problem to the study of the following two functional equations: $ h(\min(xg(y),1)) = \min(h(x)+ h(xy),1)$, $x \in (0,1)$, $y \in (0,1]$, and $ h(xg(y)) = h(x)+ h(xy)$, $x,y \in (0, \infty)$, in the class of increasing bijections $h\colon [0,1] \to [0,1]$ with an increasing function $g\colon (0,1] \to [1, \infty)$ and in the class of monotonic bijections $h\colon (0, \infty) \to (0, \infty)$ with a function $g\colon (0, \infty) \to (0, \infty)$, respectively. A description of solutions in more general classes of functions (including nonmeasurable ones) is presented.

5

On some functional equations with a restricted domain, II

60%

Ger R.

Fundamenta Mathematicae

|

1978

|

tom 98

|

nr 3

249-272

6

Convex functions of higher orders in Euclidean spaces

60%

Ger R.

Annales Polonici Mathematici

|

1971-1972

|

tom 25

|

nr 3

293-302

7

On Mikusiński-Pexider functional equation

50%

Baron K., Ger R.

Colloquium Mathematicum

|

1973

|

tom 28

|

nr 2

307-312

8

On some functional equations with a restricted domain

50%

Ger R.

Fundamenta Mathematicae

|

1975

|

tom 89

|

nr 2

131-149

9

p-convex iteration groups

41%

Ger R., Smajdor A.

Fundamenta Mathematicae

|

1976

|

tom 91

|

nr 1

29-38

10

On almost polynomial functions

40%

Ger R.

Colloquium Mathematicum

|

1971-1972

|

tom 24

|

nr 1

95-101

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3 Colloquium Mathematicum

3 Commentationes Mathematicae

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1 Annales Polonici Mathematici

10 Ger R.

2 Sablik M.

1 Baron K.

1 Kochanek T.

1 Kuczma M. E.

1 Niemyska W.

1 Smajdor A.

1 2015

1 2014

1 2013

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1 1978

1 1976

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An inconsistency equation involving means

Mean values for vector valued functions and corresponding functional equations

Errata list for "Mean values for vector valued functions and corresponding functional equations" (Commentationes Mathematicae 53(2) (2013), 355-369)

On two functional equations connected with distributivity of fuzzy implications

On some functional equations with a restricted domain, II

Convex functions of higher orders in Euclidean spaces

On Mikusiński-Pexider functional equation

On some functional equations with a restricted domain

p-convex iteration groups

On almost polynomial functions