Fundamental Questions and New Counterexamples for b-Metric Spaces and Fatou Property

Abstract

In this paper, we give new examples to show that the continuity actually strictly stronger than the Fatou property in b-metric spaces. [...]

A Fixed Point Theorem for Generalized Ćirić-Type Contraction in Kaleva–Seikkala’s Type Fuzzy b-Metric Spaces

“…As we have seen that the metric d in b-MS is discontinuous in general and d does not have Fatou property. Moreover, it follows that Fatou property is strictly weaker than continuity (see [21]). It is easily seen that the metric D has the analogous property in the KS-FbMS (M, D, L, R, b).…”

Common Fixed Point of (ψ, β, L)-Generalized Contractive Mapping in Partially Ordered b-Metric Spaces

“…Otherwise, for more notions such as b-convergence, b-completeness, b-Cauchy sequence and b-continuity in b-metric spaces, the reader may refer to [1,[4][5][6][7][8][9][10][11]13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references mentioned therein.…”

“…He provided the generalized BCP in b-metric space. From then on, a large number of papers have considered fixed point theory and its applications or variational methods for singlevalued and multi-valued operators in b-metric spaces (the reader may see [5][6][7][8][9][10] and the related references therein). The mappings satisfying certain contractive conditions can be utilized to establish the existence of solutions to all kinds of operator equations such as integral equations, differential equations and fractional differential equations.…”

On \({\mathbb{BID}}\)-Cone b-Metric Spaces over Banach Algebras: New Topological Properties and Fixed Point Theorems

“…They also investigated topological properties on cones. Afterwards, some topological properties of cone metric spaces developed into one of the centers of strong research activities (see [8][9][10][11][12][13][14][15][16][17][18]). In 2014, Xu and Radenović [19] considered topological properties on cones and algebraic cones in the setting of cone metric spaces over Banach algebras introduced by Liu and Xu [20].…”