Convergence of set-valued mappings: Equi-outer semicontinuity

Bagh, Adib; Wets, Roger J.-B.

doi:10.1007/bf00436110

Cited by 15 publications

(19 citation statements)

References 11 publications

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“…If Y is compact then this notion coincides with the notion of even-outer-semicontinuity. In general, however this notion turns out to be too constringent for applications purposes [4].…”

Section: Continuity and Equicontinuitymentioning

confidence: 99%

“…The notion of even-outer-semicontinuity for set-valued maps is introduced and compared with related ones from [4] and [11]. The coincidence of these notions provides a new characterization of compactness and of local compactness.…”

mentioning

confidence: 99%

“…Graph convergence (that is Painlevé-Kuratowski convergence of graphs) of set-valued maps was studied in many books and papers (see for example [1,2,4,9,11]). In this topic we can include also graph convergence of single-valued maps [5,12,13], epiconvergence of lower semicontinuous functions [4,6,7] as well as Painlevé-Kuratowski convergence of graphs of partial maps [8] .…”

mentioning

confidence: 99%

“…In this topic we can include also graph convergence of single-valued maps [5,12,13], epiconvergence of lower semicontinuous functions [4,6,7] as well as Painlevé-Kuratowski convergence of graphs of partial maps [8] . In the books of Attouch [1], Aubin-Frankowska [2] 1991 Mathematics Subject Classification.…”

mentioning

confidence: 99%

“…In our paper we study the relationship between graph convergence and pointwise one introducing the notion of even-outer-semicontinuity which allows us to pass from one convergence to the other. Other notions of joint continuity (see for example [4,9,11]) are compared with ours. The relationship between the notions of continuous convergence and graph convergence is analysed too.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Graph Convergence of Set-Valued Maps and its Relationship to Other Convergences

Prete¹,

Iorio²,

Holá³

2000

Journal of Applied Analysis

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Abstract. The notion of even-outer-semicontinuity for set-valued maps is introduced and compared with related ones from [4] and [11]. The coincidence of these notions provides a new characterization of compactness and of local compactness. The following result is proved: Let X be a topological space, Y a uniform space, {Fσ : σ ∈ Σ} be a net of set-valued maps from X to Y and F be a set valued map from X to Y . Then any two of the following conditions imply the third: (1) the net {Fσ : σ ∈ Σ} is evenly-outer semicontinuous; (2) the net {Fσ : σ ∈ Σ} is graph convergent to F ; (3) the net {Fσ : σ ∈ Σ} is pointwise convergent to F . This theorem generalizes some results from [4] and [11].Graph convergence (that is Painlevé-Kuratowski convergence of graphs) of set-valued maps was studied in many books and papers (see for example [1,2,4,9,11]). In this topic we can include also graph convergence of single-valued maps [5,12,13], epiconvergence of lower semicontinuous functions [4,6,7] as well as Painlevé-Kuratowski convergence of graphs of partial maps [8] . In the books of Attouch [1], Aubin-Frankowska [2] 1991 Mathematics Subject Classification. 54C60, 54B20.

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“…If Y is compact then this notion coincides with the notion of even-outer-semicontinuity. In general, however this notion turns out to be too constringent for applications purposes [4].…”

Section: Continuity and Equicontinuitymentioning

confidence: 99%

mentioning

confidence: 99%