Abstract

We study I\mathcal{I}-convergence of sequences of functions. Mainly, we study Vitali type I\mathcal{I}-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 I\mathcal{I}-sequentially compact subsets of p-Dunford integrable functions. We study uniform I\mathcal{I}-convergence of sequences of p-Bochner, p-Dunford and p-Pettis integrable functions, and weak uniform I\mathcal{I}-convergence of sequences of p-Dunford and p-Pettis integrable functions, and discuss how they are related to the p-Bochner and p-Pettis I\mathcal{I}-convergence. I\mathcal{I}-convergence of compact mappings are studied with special emphasis to compact linear operators on normed linear spaces. We also study I\mathcal{I}-exhaustiveness, I\mathcal{I}-weak exhaustiveness and I\mathcal{I}-α\alpha-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.

Author information

Contact details are reproduced from the original publication and may be historical.

Lakshmi Kanta Dey

Department of Mathematics, National Institute of Technology, Durgapur, India

lakshmikdey@yahoo.co.in

Keywords

  • I-convergence in measure
  • p-Bochner I-uniformly integrable
  • p-Pettis I-uniformly integrable
  • p-Bochner delta-I-Cauchy
  • p-Pettis delta-I-Cauchy

Mathematics Subject Classification

26A42, 28B05, 28A45; 46G10

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Suggested citation

P. Mondal, L. K. Dey, S. J. Ali. “I-Convergence of Sequences of p-Bochner, p-Dunford and p-Pettis Integrable Functions with Values in a Banach Space.” Journal of Convex Analysis 32 (2025), No. 4, 1091–1116. https://doi.org/10.68381/jca32058

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