Positivity https://doi.org/10.1007/s11117-018-0590-5 Positivity Some topological properties and ﬁxed point results in cone metric spaces over Banach algebras 1 1 Huaping Huang · Guantie Deng · Stojan Radenovic´ Received: 21 December 2017 / Accepted: 23 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract This note is intended as an attempt at presenting some topological properties in cone metric spaces over Banach algebras. Moreover, the corresponding ﬁxed point results are given. In addition, the P property, T -stability of Picard’s iteration, well- posedness of ﬁxed point problems are also displayed. Our results complement and generalize some previous results in the existing literature. Keywords c-Sequence · θ-Sequence · T -stability · P property · Well-posedness Mathematics Subject Classiﬁcation 47H10 · 54H25 1 Introduction Metric spaces are of great values both in theory and applications, for instance, ﬁxed point theory based on metric spaces is one of the most inﬂuential areas in pure and applied mathematics. However, with the progress of science and technology, the theory of metric spaces has been far from meeting the needs of people. Because of these B Guantie Deng firstname.lastname@example.org Huaping Huang email@example.com Stojan Radenovic´ firstname.lastname@example.org School of Mathematical Sciences, Beijing Normal University,
Positivity – Springer Journals
Published: May 29, 2018
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