Open AccessCommon new fixed point results on b-cone Banach spaces over Banach algebras
Author(s) -
Hojjat Afshari,
Hadi Shojaat,
Andreea Fulga
Publication year - 2022
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2022.15571
Subject(s) - mathematics , cone (formal languages) , banach space , pure mathematics , metric space , fixed point theorem , norm (philosophy) , discrete mathematics , algorithm , political science , law
Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of ϕ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by usingϕ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions andfollowing their work with introducing two mappings $\mathcal{T}$ and $\mathcal{S}$ we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.