Intergenerational equity: sup, inf, lim sup, and lim inf

Chambers, Christopher P.

doi:10.1007/s00355-008-0321-0

Cited by 14 publications

(5 citation statements)

References 27 publications

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“…In this paper, used the notions of lim sup, and lim inf from [22], I generalize this definition as follows: Definition 2.2. Let (p i ) a sequence of strictly positive real numbers and A. Bucur for all n. A sequence (x n ) ⊂ X was said to be lower strong fractional weighted mean convergent to L if…”

Section: Definitions and Notationsmentioning

confidence: 99%

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About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

Bucur¹

2023

JAMP

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In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.

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Section: Definitions and Notationsmentioning

confidence: 99%

“…in [1] [2] [17] [20]). In [21], Mursaleen and Edely obtained Connor's [22] result for double sequences. In [23], Șahiner et al present results for triple sequences.…”

Section: Introductionmentioning

confidence: 98%

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

Bucur¹

2023

JAMP

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“…In particular, the swf satisfies a "uniform" Pareto principle in the sense that for all x, y ∈ X and ε > 0, if x t ≥ y t + ε for all t ∈ N, then w 4 (x) > w 4 (y). For more on the axiomatic basis for related swfs, see Chambers (2009) and Sakai (2016).…”

Section: Weakening Restricted Dominancementioning

confidence: 99%

How stationarity contradicts intergenerational equity

2020

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We show how the condition of stationarity may contradict intergenerational equity. By formalizing the intuition that less sensitivity remains for the continuation of the stream if sensitivity for the interests of the present is combined with stationarity, we point out conflicts (a) between stationarity and the requirement of not letting the present be dictatorial, and (b) between stationarity and equal treatment of generations. We use the results to interpret the non-stationarity of the Chichilnisky and Rank-discounted utilitarian social welfare functions. Non-stationarity combined with time invariance leads to time inconsistency. We illustrate how such non-stationary social welfare functions can be applied in the Ramsey model if time invariance is imposed.

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“…Both these rules satisfy strong anonymity, monotonicity (if x ≥ y, then x y), continuity with respect to the sup-topology, and Hammond equity. Characterizations are obtained by Lauwers (1997c) and Chambers (2009). 19 We close this section with the rank-discounted utilitarian rule.…”

Section: Strong Anonymitymentioning

confidence: 99%

The Axiomatic Approach to the Ranking of Infinite Streams

Lauwers

2016

The Economics of the Global Environment

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The history of the axiomatic approach to the ranking of infinite streams starts with Koopmans' (1960) characterization of the discounted utilitarian rule. This rule, however, meets Chichilnisky's axiom of dictatorship of the present and puts future generations offside. Recently, Lauwers (2010a) and Zame (2007) have uncovered the impossibility to combine in a constructible way the requirements of equal treatment, sensitivity, and completeness. This contribution presents and discusses different axioms proposed to guide the ranking of infinite streams and the criteria they imply. The literature covered in this overview definitely points towards a set of meaningful alternatives to discounted utilitarianism. JEL Classification Number: D71, D81. 1 In his review on intergenerational equity, Asheim (2010, section 3.2) coins this result as the Lauwers-Zame impossibility theorem. 2 I want to mention already here that the combination of continuity with respect to the sup-topology and representability does not guarantee that the ranking rule is constructible. The other way around, the representation of a non-constructible ordering, is in itself a non-constructible object.

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Intergenerational equity: sup, inf, lim sup, and lim inf

Cited by 14 publications

References 27 publications

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

How stationarity contradicts intergenerational equity

The Axiomatic Approach to the Ranking of Infinite Streams

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