2023/09/25 by P. Gayathri, Gayathri, P., Vamsinadh Thota +1
Computer Science · Mathematics · #41A65 #46B20 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2309.14224
openalex publication_date 2023/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce two notions called k-weakly uniform rotundity (k-WUR) and k-weakly locally uniform rotundity (k-WLUR) in real Banach spaces. These are natural generalizations of the well-known concepts k-UR and WUR. By introducing two best approximation notions namely k-weakly strong Chebyshevity and k-weakly uniform strong Chebyshevity, we generalize some of the existing results to k-WUR and k-WLUR spaces. In particular, we present characterizations of k-WUR spaces in terms of k-weakly uniformly strong Chebyshevness. Also, the inheritance of the notions k-WUR and k-WLUR by quotient spaces are discussed. Further, we provide a necessary and sufficient condition for an infinite ℓp-product space to be k-WUR (respectively, k-WLUR). As a consequence, we observe that the notions WUR and k-WUR coincide for an infinite ℓp-product of a Banach space.