Journal of Convex Analysis 32 (2025), No. 4, 1091--1116
Copyright Heldermann Verlag 2025
I-Convergence of Sequences of p-Bochner, p-Dunford and p-Pettis Integrable Functions with Values in a Banach Space
Pratikshan Mondal
Department of Mathematics, Durgapur Government College, Burdwan, India
real.analysis77@gmail.com
Lakshmi Kanta Dey
Department of Mathematics, National Institute of Technology, Durgapur, India
lakshmikdey@yahoo.co.in
Sk. Jaker Ali
Department of Mathematics, Bolpur College, Bolpur, Birbhum, India
ali.jaker2015@gmail.com
We study I-convergence of sequences of functions. Mainly, we study Vitali type 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-sequentially compact subsets of p-Dunford integrable functions. We study uniform I-convergence of sequences of p-Bochner, p-Dunford and p-Pettis integrable functions, and weak uniform 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-convergence. I-convergence of compact mappings are studied with special emphasis to compact linear operators on normed linear spaces. We also study I-exhaustiveness, I-weak exhaustiveness and I-α-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.
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.
MSC: 26A42, 28B05, 28A45; 46G10.
[ Fulltext-pdf (188 KB)] for subscribers only.