Surprises and Counterexamples in Real Function Theory

Rajwade, A. R.; Bhandari, Ashwani K.

doi:10.1007/978-93-86279-35-4

Cited by 4 publications

(3 citation statements)

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“…In [RB,Chapter 7], it is proved that this limit exists for e −e ≤ x ≤ e 1/e and is mutually inverse to the function…”

Section: Extended Dimensioned Numbersmentioning

confidence: 99%

Application of dimensioned numbers to functional equations

Hayashi

2014

ESAIM: Proc.

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Abstract. In this paper, we introduce the notion of dimensioned numbers and extended dimensioned numbers. The notion of dimensioned numbers originates in geometric measurements, and it can be used to describe iterated exponential functions of a single variable. We apply the theory of dimensioned numbers to solving some functional equations of a single variable.Résumé. Dans cet article, nous introduisons la notion de nombres dimensionnés et prolongés nombres dimensionnés. La notion de nombres dimensionnés vient de mesures géométriques, et ils peuventêtre utilisés pour représenter les fonctions exponentielles répétées d'une seule variable. Nous appliquons la théorie des nombres dimensionnésà la résolution de certaineséquations fonctionnelles d'une seule variable.

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“…In [RB,Chapter 7], it is proved that this limit exists for e −e ≤ x ≤ e 1/e and is mutually inverse to the function…”

Section: Extended Dimensioned Numbersmentioning

confidence: 99%

Application of dimensioned numbers to functional equations

Hayashi

2014

ESAIM: Proc.

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“…We hope that this note is of interest to those who want to flavour their lectures with some unexpected or even weird examples. In this context we also refer the reader to the books of Appell [2], Gelbaum/Olmsted [9] and Rajwade/Bhandari [15] which contain rich collections of counterexamples and pecularities from many fields of real analysis.…”

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confidence: 99%

“…For a more detailed discussion of five different definitions of inflection point we refer to[15, Section 5.5]. Here we just want to point out some noteworthy aspects.…”

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confidence: 99%

Some counterexamples on the behaviour of real-valued functions and their derivatives

Grahl,

Nevo

2013

Preprint

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We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict minimum doesn't have to be decreasing to the left nor increasing to the right of the minimum, we present a function f whose derivative is discontinuous at one point x 0 and oscillates only above f ′ (x 0 ) (i.e. f ′ has a strict minimum at x 0 ), we compare several definitions of inflection point, and we discuss a general version of the theorem on the derivative of inverse functions where continuity of the inverse function is assumed merely at one point.

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On iterative premium calculation principles under Cumulative Prospect Theory

Kałuszka

Krzeszowiec

2013

Insurance: Mathematics and Economics

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Surprises and Counterexamples in Real Function Theory

Cited by 4 publications

References 0 publications

Application of dimensioned numbers to functional equations

Application of dimensioned numbers to functional equations

Some counterexamples on the behaviour of real-valued functions and their derivatives

On iterative premium calculation principles under Cumulative Prospect Theory

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