Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications

The Proximal Point Algorithm for Monotone Vector Fields on Complete Geodesic Spaces

Shuta Sudo — 2025-05-01

In this paper, we deal with monotone vector fields defined on geodesic spaces and their zero point approximation method. In an appropriate setting, we can define the resolvent operator for a given monotone vector field, and then that operator has many useful properties which are effective for the fixed point theory. We will show an approximation theorem for a monotone vector field with the canonical proximal point algorithm.

Approximating Endpoints of Multi-Valued Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces Using a Novel Iteration Process

Thanomsak Laokul — 2025-05-06

In this paper, we propose a modified iteration process for approximating the endpoints of multi-valued nonexpansive mappings in 2-uniformly convex hyperbolic spaces, extending the framework of uniformly convex Banach spaces. We establish a \(\Delta\)-convergence theorem for the iterative sequence and, under sufficient conditions, prove strong convergence theorems. These findings extend and improve upon the work of Makbule Kaplan Ozekes and others. ¨

Extending the Scope of the Fractional Hardy Integral Inequality

Christophe Chesneau — 2025-05-06

In this article, we establish two theorems that generalize the fractional Hardy integral inequality by incorporating several intermediate functions and parameters. The assumptions made are tractable. Some of them can be related to the notions of sub-additivity and sub-multiplicativity. The proofs are self-contained, without intermediate results, and all details are given. We thus extend the applicability of a classical integral inequality and offer new potential applications in mathematical analysis.