I-Convergence of Sequences of p-Bochner, p-Dunford and p-Pettis Integrable Functions with Values in a Banach Space

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.