Nermin Okicic

• PhD
• Professor at 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...

In this paper we consider the semilinear singularly perturbed reaction--diffusion boundary value problem. In the first part of the paper a difference scheme is given for the considered problem. In the main part of the paper a cubic spline is constructed and we show that it represents a global approximate solution of the our problem. At the end of t...

In this article we introduce the new modulus $\triangle'_{X,\phi}(\varepsilon)$, 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 no...

The textbook "Metric spaces" was written and accepted for use as a university textbook at the University of Tuzla. It is written in Bosnian and intended for native Bosnian speakers, as is the description below. CIP - Katalogizacija u publikaciji Nacionalna i univerzitetska biblioteka Bosne i Hercegovine, Sarajevo 515.124(075.8) Iako možda svako od...

The textbook "Elements of mathematical logic with application in computer science" was written and accepted for use as a university textbook at the University of Tuzla. It is written in Bosnian and intended for native Bosnian speakers, as is the description below. CIP - Katalogizacija u publikaciji Nacionalna i univerzitetska biblioteka Bosne i H...

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)).

We deal with quadratic metric-affine gravity (QMAG), which is an alter- native theory of gravity and present a new explicit representation of the eld equa- tions of this theory. In our previous work we found new explicit vacuum solutions of QMAG, namely generalised pp-waves of parallel Ricci curvature with purely tensor torsion. Here we do not make...

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)).

We consider the singularly perturbed selfadjoint one-dimensional semilinear reaction-diffusion problem () () 2 : , L y y x f x y ε ε ′′ = = , on () 1 , 0 () 0 0 = y ; () 0 1 = y , where f(x,y) is a non-linear function. For this problem, using the spline-method with the natural choice of functions, a new difference scheme is given on a non-uniform m...

In this paper we consider semilinear elliptic Dirichlets boundary value problem with small parameter, well known as singularly perturbed semilinear reaction-diffusion problem. Using theory of projection-mesh methods, precisely using the Galerkin method with natural choice of test function, the given boundary problem is discretized and we get a disc...

In the present paper we give some propositions about conditions for compactness and condensation of the nonlinear superposition operator (1) in l p,σ spaces.

In this paper we describe the L-characteristic L(F , P) (where P is an acting or a boundedness condition) of the nonlinear superposition operator F generated by a function f (s, u), between two weighted l p,σ spaces of functions x from N to R. We show that the L-characteristic of the operator F has an important interpolation property, namely L(F ,...

The aim of this paper is to explore in some detail the second order linear ordinary differential equation with real or complex periodic coefficients, also known as the Hill’s equation, with some emphasis on stability and instability intervals and explore two related self-adjoint eigenvalue problems leading to the two final results which enable us t...

This paper considers a non-linear superposition operator on weighted Banach spaces lp,σ, where σ is the weight function with the property that: (∀n ∈ N)σ(n) ≥ 1. We present the necessary and sufficient conditions of action of the operator from lp,σ to lq,τ , 1 ≤ p, q ≤ ∞, and also the L-characteristic of the considered action of the operator.