Volume 46, Issue 1

The key result in this paper shows that autocontinuity is a sufficient and necessary condition on a monotone measure such that convergence in measure of a sequence of measurable functions implies convergence of the corresponding sequence of seminormed fuzzy integrals of those measurable functions. Our work is an improvement of several previously published results.

In this paper, a weak convergence theorem is proved to find out the solution of variational inequality problem for a mapping which is monotone as well as Lipschitz continuous in Hilbert space. This result can also be used to determine the solutions of constrained convex optimization and split feasibility problems.

In this paper, we focus on investigating the existence of mild solutions and the stability analysis of fractional evolution equations involving finite time delay and maxima. Our approach relies on tools such as the measure of non-compactness, the concept of p {{p}} -set contractions, and the Banach contraction principle. Additionally, we employ a generalized form of Gronwall’s inequality to examine various types of stability. To demonstrate the applicability of our theoretical findings, a concrete example is provided.