In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

In this paper we continue our investigation concerning the hyperbolic geometry on the noncommutative ball [B(H)]−1 := n (X1, . . . ,Xn) ∈ B(H) n : ‖X1X ∗ 1 + · · ·+XnX ∗ n‖ 1/2 ≤ 1 o , where B(H) is the algebra of all bounded linear operators on a Hilbert space H, and its implications to noncommutative function theory. The central object is an intertwining operator LB,A of the minimal isometric...

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.

a common fixed point result for weakly increasing mappings satisfying generalized contractive type of zhang in ordered metric spaces are derived.

in this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy m-complete metric spaces. we also give an affirmative partial answer to a question posed by wardowski [d. wardowski, fuzzy contractive mappings and fixed points in fuzzy metric spaces, fuzzy set syst., {bf 222}(2013), 108-114].some examples are also g...

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

Let Fq denote a finite field with q elements and let V = (Fq)m,n be the Fq-vector space of matrices over Fq of type (m,n). On V we define the so-called rank metric distance by d(A,B) = rank(A−B) for A,B ∈ V . Clearly, the distance d is a translation invariant metric on V . A subset C ⊆ V endowed with the metric d is called a rank metric code with minimum distance d(C) = min {d(A,B) | A 6= B ∈ V...

The symmetric group S , is a metric space with distance d(a , b ) = IE(a-'b)( where E ( c ) is the set of points moved by c E S,. Let L be a given subset of {I. 2, . . . , n}, a permutation clique A = A(L, n ) is any subset A c S , with d(a, b ) E L whenever a, b E A , a # b. We give a framework of new and known information o n some special A = A ( L , n): maximal, largest, largest subgroups of...

We look at a model of random graphs suggested by Gilbert: given an integer n and δ > 0, scatter n vertices independently and uniformly on a metric space, and then add edges connecting pairs of vertices of distance less than δ apart. We consider the asymptotics when the metric space is the interval [0, 1], and δ = δ(n) is a function of n, for n→∞. We prove that every upwards closed property of (...

We consider a new construction, the weak Delaunay triangulation of a finite point set in a metric space, which contains as a subcomplex the traditional (strong) Delaunay triangulation. The two simplicial complexes turn out to be equal for point sets in Euclidean space, as well as in the (hemi)sphere, hyperbolic space, and certain other geometries. There are weighted and approximate versions of ...