Since 1964, when I.A. Perov introduced the so-called generalized metric space where d(x,y) is an element of vector Rm, many researchers have considered various contractive conditions in this type space. In paper, we generalize, extend and unify some those established results. We are primarily concerned with examining existence a fixed point mapping from X to itself, but if (x,y) belongs relatio...

It is well known that linear rank-metric codes give rise to q-polymatroids. Analogously matroid theory, one may ask whether a given q-polymatroid representable by code. We provide an answer presenting example of q-matroid not any code and, via relation paving matroids, examples various q-matroids are $${{\mathbb {F}}}_{q^m}$$ -linear codes. then go on and introduce deletion contraction for q-po...

Abstract Let $(X,B)$ be a pair, and let $f \colon X \rightarrow S$ contraction with $-({K_{X}} + B)$ nef over S . A conjecture, known as the Shokurov–Kollár connectedness principle, predicts that $f^{-1} (s) \cap \operatorname {\mathrm {Nklt}}(X,B)$ has at most two connected components, where $s \in is an arbitrary schematic point $\operatorname denotes non-klt locus of In this work, we prove c...

Let (X,H) be a pair of a smooth rational surface X and an ample divisor H on X . Assume that (KX , H) < 0. Let MH(r, c1, χ) be the moduli space of semi-stable sheaves E of rk(E) = r, c1(E) = c1 and χ(E) = χ. To consider relations between moduli spaces of different invariants is an interesting problem. If (c1, H) = 0 and χ ≤ 0, then Maruyama [Ma2], [Ma3] studied such relations and constructed a ...

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, we introduce a cone generalized semi-cyclicφ−contraction maps and prove best proximity points theorems for such mapsin cone metric spaces. Also, we study existence and convergence results ofbest proximity points of such maps in normal cone metric spaces. Our resultsgeneralize some results on the topic.