DOI: 10.68381/jca32058 ISSN: 0944-6532
I-Convergence of Sequences of p-Bochner, p-Dunford and p-Pettis Integrable Functions with Values in a Banach Space
Pratikshan Mondal, Lakshmi Kanta Dey, Sk. Jaker Ali
We study
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-convergence of sequences of functions. Mainly, we study Vitali type
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-convergence theorems for sequences of p-Bochner, p-Dunford and p-Pettis integrable functions with values in a Banach space. With the help of these theorems, we characterize p-Bochner relatively compact subsets of p-Bochner integrable functions and p-Pettis relatively
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-sequentially compact subsets of p-Dunford integrable functions. We study uniform
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-convergence of sequences of p-Bochner, p-Dunford and p-Pettis integrable functions, and weak uniform
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-convergence of sequences of p-Dunford and p-Pettis integrable functions, and discuss how they are related to the p-Bochner and p-Pettis
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-convergence.
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-convergence of compact mappings are studied with special emphasis to compact linear operators on normed linear spaces. We also study
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-exhaustiveness,
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-weak exhaustiveness and
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-
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-convergence of sequences of metric space-valued functions defined on a metric space, and sequences of p-Dunford integrable functions are discussed in this perspective.