A New fuzzy McShane integrability

2021 ◽  
Vol 71 (3) ◽  
pp. 631-648
Author(s):  
Redouane Sayyad
Keyword(s):  
Banach Spaces ◽  
Pettis Integral ◽  
Linear Topology ◽  
Mcshane Integral

Abstract We introduce the notion of the fuzzy McShane integral in the linear topology sense and we discuse its relation with the fuzzy Pettis integral introduced recently by Chun-Kee Park in [On the Pettis integral of fuzzy mappings in Banach spaces, Commun. Korean Math. Soc. 22 (2007), 535–545].

scholarly journals Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Luisa Di Piazza ◽  
Valeria Marraffa
Keyword(s):  
Banach Spaces ◽  
Pettis Integral ◽  
Fuzzy Mapping ◽  
Pettis Integrability

AbstractIn this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable.

scholarly journals A Note on the Paper ”Fractional Order Pettis Integral Equations with Multiple Time Delay in Banach Spaces” by M. Benchohra and F.-Z. Mostefai

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Mieczysław Cichoń
Keyword(s):  
Integral Equation ◽  
Time Delay ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Weak Topology ◽  
Classical Case ◽  
Existence Results ◽  
Multiple Time ◽  
Pettis Integral

Abstract On a recent paper Benchohra and Mostefai [2] presented some existence results for an integral equation of fractional order with multiple time delay in Banach spaces. In contrast to the classical case, when assumptions are expressed in terms of the strong topology, they considered another case, namely with the weak topology. It has some consequences for the proof. We present here some comments and corrections.

scholarly journals Measurable selectors and set-valued Pettis integral in non-separable Banach spaces

2009 ◽  
Vol 256 (3) ◽  
pp. 673-699 ◽  
Author(s):  
B. Cascales ◽  
V. Kadets ◽  
J. Rodríguez
Keyword(s):  
Banach Spaces ◽  
Pettis Integral

A variational mcshane integral characterization of the Radon-Nikodym property

2013 ◽  
Vol 63 (3) ◽  
Author(s):  
Sokol Kaliaj
Keyword(s):  
Banach Spaces ◽  
Lebesgue Measure ◽  
Absolutely Continuous ◽  
Mcshane Integral ◽  
Nikodym Property ◽  
Interval Functions

AbstractWe present a new characterization of Banach spaces possessing the Radon-Nikodym property in terms of additive interval functions whose McShane variational measures are absolutely continuous with respect to the Lebesgue measure.

Fractional Order Pettis Integral Equations with Multiple Time Delay in Banach Spaces

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Mouffak Benchohra ◽  
Fatima-Zohra Mostefai
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Time Delay ◽  
Banach Spaces ◽  
Fractional Order ◽  
Existence Of Solutions ◽  
Multiple Time ◽  
Pettis Integral ◽  
Measure Of Weak Noncompactness ◽  
Pettis Integrability

Abstract This paper is devoted to study the existence of solutions under the Pettis integrability assumption for an integral equation of fractional order with multiple time delay in Banach space by using the technique of measure of weak noncompactness. Mathematics Subject Classification 2010: 26A33, 34A08.

scholarly journals The product of vector-valued measures

1973 ◽  
Vol 8 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Scalar Field ◽  
Banach Spaces ◽  
Vector Measure ◽  
Sufficient Condition ◽  
Pettis Integral ◽  
Necessary And Sufficient Condition ◽  
Bilinear Map ◽  
Scalar Measure ◽  
Necessary And Sufficient ◽  
Vector Valued

Let M (N) be a σ–algebra of subsets of a set S (T) and let X, Y be Banach spaces with (,) a continuous bilinear map from X × Y into the scalar field. If μ: M → X (v: N → Y) is a vector measure and λ is the scalar measure defined on the measurable rectangles A × B, A ∈ M, B ∈ N, by λ(A×B) = 〈μ(A), v(B)〉, it is known that λ is generally not countably additive on the algebra generated by the measurable rectangles and therefore has no countably additive extension to the σ-algebra generated by the measurable rectangles. If μ (v) is an indefinite Pettis integral it is shown that a necessary and sufficient condition that λ have a countable additive extension to the σ-algebra generated by the measurable rectangles is that the function F: (s, t) → 〈f(s), g(t)〉 is integrable with respect to α × β.

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