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Takahashi introduced the concept of convex structure in a metric space $(X,d)$ as a mapping $\mathcal{W}:X^2\times[0,1]\longrightarrow X$ satisfying $$d\left(z,\mathcal{W}(x,y,\alpha)\right)\leq\alpha …

The definitions of Roberts orthogonality (B D Roberts) and $\alpha$-Isosceles orthogonality (Alonso & Benitez) seems to be identical to me. Can anyone point me out the difference between the two ortho …

Is Birkhoff-James orthogonality an orthogonality in the sense of Ratz? Orthogonality in the sense of Ratz: Suppose $X$ is a real vector space with $\dim X\geq2$ and $\perp$ is a binary relation on $ …

A b-metric is defined similar to a metric in which the triangle inequality is replaced by the inequality $$d(x,z)\leq s\Big[d(x,y)+d(x,z)\Big]\quad\forall\ x,y,z$$ where $s\geq1$. There is an example …

I came across the statement ``Every closed and convex subset of a uniformly convex b-metric space is Chebyshev'' in [1]. Here, the term `convex' is in the sense of Takahashi. I tried looking up for th …