Fundamental theorem of calculus under weaker forms of primitive

In this paper we will present abstract versions of fundamental theorem of calculus (FTC) in the setting of Kurzweil - Henstock integral for functions taking values in an infinite dimensional locally convex space. The result will also be dealt with weaker forms of primitives in a widespread setting o...

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Published in:Acta universitatis sapientiae. Mathematica Vol. 10; no. 1; pp. 101 - 111
Main Authors: Lone, Nisar A., Chishti, T. A.
Format: Journal Article
Language:English
Published: Cluj-Napoca Sciendo 01.08.2018
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:
Bochner integral
Frechet space
Fundamental theorem of calculus
Kurzweil - Henstock intgeral
Primary 46G10
Secondary 46G12
ISSN:2066-7752, 1844-6094, 2066-7752
Online Access:Get full text
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Summary:In this paper we will present abstract versions of fundamental theorem of calculus (FTC) in the setting of Kurzweil - Henstock integral for functions taking values in an infinite dimensional locally convex space. The result will also be dealt with weaker forms of primitives in a widespread setting of integration theories generalising Riemann integral.
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ISSN:2066-7752
1844-6094
2066-7752
DOI:10.2478/ausm-2018-0009