DIFFERENT FORMS OF CONVEXITY IN METRIC LINEAR SPACES HARPREET K. GROVER, T.D.NARANG, SHELLY GARG | ||||
| Electronic Journal of Mathematical Analysis and Applications | ||||
| Volume 13, Issue 1, 2025, Page 1-11 PDF (511.03 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/ejmaa.2025.398048 | ||||
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| Abstract | ||||
| Abstract. Various forms of convexity in normed linear spaces that fall between strict and uniform convexity, such as the 2R property, local uniform convexity, compact local uniform convexity, and mid-point local uniform convexity, have sparked considerable interest over the years and have been thoroughly investigated in the literature. The notion of strict convexity was extended to metric linear spaces by Albinus in 1968, and that of uniform convexity by Ahuja et al. in 1977. In this paper, we extend the other mentioned forms of convexity to metric linear spaces. We explore the metric linear spaces that have these properties and establish inter-relationships between these spaces. We also give a characterization of strictly convex metric linear spaces. | ||||
| Keywords | ||||
| metric linear space; strict convexity; rotundity; uniform convexity; local uniform convexity; compact local uniform convexity; mid-point local uniform convexity; 2R property | ||||
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