Common new fixed point results on b-cone Banach spaces over Banach algebras




common fixed point, ϕ-operator, cone b-norm, cone b-Banach space


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.


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Author Biographies

Hojjat Afshari, University of Bonab

Department of Mathematics, Faculty of Sciences

Hadi Shojaat, Farhangian University

Department of Mathematics

Andreea Fulga, Transilvania University of Brasov

Department of Mathematics and Computer Sciences


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How to Cite

H. Afshari, H. Shojaat, and A. Fulga, “Common new fixed point results on b-cone Banach spaces over Banach algebras”, Appl. Gen. Topol., vol. 23, no. 1, pp. 145–156, Apr. 2022.