A convexity of functions on convex metric spaces of Takahashi and\n applications

2015/08/30 by Ahmed A. Abdelhakim, Abdelhakim, Ahmed A. · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1508.07652

openalex publication_date 2015/08/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We quickly review and make some comments on the concept of convexity in\nmetric spaces due to Takahashi. Then we introduce a concept of convex structure\nbased convexity to functions on these spaces and refer to it as W-convexity.\nW-convex functions generalize convex functions on linear spaces. We discuss\nillustrative examples of (strict) W-convex functions and dedicate the major\npart of this paper to proving a variety of properties that make them fit in\nvery well with the classical theory of convex analysis. Finally, we apply some\nof our results to the metric projection problem and fixed point theory.\n

Cited by

• Uniform Convergence of Generalized Conditional Fréchet Means with Applications to Weighted Fréchet Aggregation and Exceedance Set Estimation

Related

• Segments and Convexity in Metric Spaces
• Fixed points and selections of multifunctions on spaces with convexity
• Convex analysis in normed spaces and metric projections onto convex bodies
• Convexity of sets and quadratic functions on the hyperbolic space
• On the Properties of Convex Functions over Open Sets