2020/06/07 by Kazem Haghnejad Azar, Azar, Kazem Haghnejad, Mina Matin +3
Mathematics · #46C05 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Primary 39B82 #Secondary 44B20
paper · pdf · doi:10.48550/arxiv.2006.04065
openalex publication_date 2020/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this manuscript, we will study both o-convergence in (partially) ordered vector spaces and a kind of convergence in a vector space V. A vector space V is called semi-order vector space (in short semi-order space), if there exist an ordered vector space W and an operator T from V into W. In this way, we say that V is semi-order space with respect to \W, T\. A net \xα\⊆ V is said to be \W,T\-order convergent to a vector x∈ V (in short we write xα\xrightarrow \W, T\x), whenever there exists a net \yβ\ in W satisfying yβ\downarrow 0 in W and for each β, there exists α0 such that ± (Txα-Tx) ≤ yβ whenever α≥ α0. In this manuscript, we study and investigate some properties of \W,T\-convergent nets and its relationships with other order convergence in partially ordered vector spaces. Assume that V1 and V2 are semi-order spaces with respect to \W1, T1\ and \W2, T2\, respectively. An operator S from V1 into V2 is called semi-order continuous, if xα\xrightarrow \W1, T1\x implies Sxα\xrightarrow \W2, T2\Sx whenever \xα\⊆ V1. We study some properties of this new classification of operators.