Open Access(m,q)-isometric and (m,∞)-isometric tuples of commutative mappings on a metric space
Author(s) -
Sid Mahmoud Ahmed,
Muneo Chō,
Ji Lee Eun
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2007425m
Subject(s) - mathematics , tuple , isometric exercise , commutative property , metric (unit) , bounded function , metric space , pure mathematics , isometry (riemannian geometry) , space (punctuation) , discrete mathematics , mathematical analysis , computer science , medicine , operations management , economics , physical therapy , operating system
In this paper, we introduce new concepts of (m,q)-isometries and (m,?)-isometries tuples of commutative mappings on metrics spaces. We discuss the most interesting results concerning this class of mappings obtained form the idea of generalizing the (m,q)-isometries and (m,?)-isometries for single mappings. In particular, we prove that if T = (T1,..., Tn) is an (m,q)-isometric commutative and power bounded tuple, then T is a (1,q)-isometric tuple. Moreover, we show that if T = (T1,...,Td) is an (m,?)- isometric commutative tuple of mappings on a metric space (E,d), then there exists a metric d? on E such that T is a (1,?)-isometric tuple on (E,d?).