Amra Rekic

• University of Tuzla

In this paper we consider the space R 2 with the river metric d * and different types of convexity of this space. We define W-convex structure in (R 2 , d *) and we give the complete characterization of the convex sets in this space. We consider some measures of noncompactness and we give the moduli of noncompactness for considered measures on this...

In this paper we consider the space $\mathbb{R}^2$ with the river metric $d^*$ and different types of convexity of this space. We define $W$-convex structure in $(\mathbb{R}^2,d^*)$ and we give the complete characterization of the convex sets in this space. We consider some measures of noncompactness and we give the moduli of noncompactness for con...

In this paper we consider some metrical and topological properties of the river metric d∗ in the plane R^2. We give the form of the metric segment and the set of all points that are equidistant from two points in (R^2, d∗). We also give the characterization of a compact sets in this space.

We consider relations between the distance of a set A and the distance of its translated set A+x from 0, for x∈A, in a normed linear space. If the relation d(0,A+x)<d(0,A)+∥x∥ holds for exactly determined vectors x∈A, where A is a convex, closed set with positive distance from 0, which we call (TP) property, then this property is equivalent to stri...

In this paper we onsider some properties of the Kuratowski measure of noncompatness on the space (R^2 , d* ), where d* is river metric. We prove the existence of the α-minimal sets in the given space, but also the strict minimalizability of the Kuratowski measure of noncompactness.

In this article we introduce the new modulus △ ′ X,φ (ε), for which we prove that in the general case is different from the classical modulus of noncompact convexity. The main result of the paper is showing the continuity of the modulus of noncompact convexity for arbitrary minimalizable (strictly minimalizable) measure of noncompactness on arbitra...

We consider Banach sequence spaces lp;� with a weighted sequence �, which are generalizations of standard sequence spaces. We investigate the relationships between these spaces for a xed p (1 � p � +1) and for di�erent weighted functions, as well as for xed � and various p; q (1 � p < q � +1). We also present the representation of bounded linear fu...

We consider the modulus of noncompact convexity ∆X,ϕ(ε) associated with the minimalizable measure of noncompactness ϕ. We present some properties of this modulus, while the main result of this paper is showing that ∆X,ϕ(ε) is a subhomogenous and continuous function on [0, (BX)) for an arbitrary minimalizable measure of compactness ϕ in the case of...

In this paper we consider modulus of noncompact convexity ΔX,φ associated with the strictly minimalizable measure of noncompactness φ. We also give some its properties and show its continuity on the interval [0, φ(BX)).

In this paper we consider modulus of noncompact convexity ∆ X,φ associated with the strictly minimalizable measure of noncompactness φ. We also give some its properties and show its continuity on the interval [0, φ(B X)).