Czechoslovak Mathematical Journal, first online, pp. 1-21
An introduction to the set-valued ap-Henstock-Kurzweil integral and its application to Volterra integral inclusions
Hemanta KALITA, Hemant Kumar NASHINE
Received October 28, 2023. Published online September 7, 2026.
Abstract: We introduce the set-valued ap-Henstock-Kurzweil integral for convex and weakly compact Banach space-valued multifunctions. We investigate several fundamental properties of this integral and establish important results concerning set-valued ap-Henstock-Kurzweil integrable mappings. As an application, we prove the existence of approximately continuous solutions for a Volterra-type integral inclusion under suitable assumptions. Our results extend and generalize several previously known theorems in the set-valued framework, since the proposed set-valued ap-Henstock-Kurzweil integral contains set-valued Henstock-Kurzweil, set-valued Bochner, and set-valued Pettis integrals as special cases.
Keywords: set-valued function; ap-Henstock-Kurzweil integral of set-valued function; measure of weak noncompactness
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