Kluvánek-Lewis-Henstock integral in a Banach space

2021/06/21 by Hemanta Kalita, Bipan Hazarika, Kalita, Hemanta +1
Computer Science · Mathematics · #46B25 #46B40 #46G10 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Primary 28B05 #Secondary 46B03

paper · pdf · doi:10.48550/arxiv.2106.11778

openalex publication_date 2021/06/21 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We investigate some properties and convergence theorem of Kluvánek-Lewis-Henstock \m-integrability for \m-measurable functions that we introduced in \citeABH. We give a \m-a.e. convergence version of Dominated (resp. Bounded) Convergence Theorem for \m. We introduce Kluvánek-Lewis-Henstock integrable of scalar-valued functions with respect to a set valued measure in a Banach space. Finally we introduce (KL)-type Dominated Convergence Theorem for the set-valued Kluvánek-Lewis-Henstock integral.

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