Volume 19, Issue 4

Abstract. The aim of this paper is to study the existence of fixed points of T -Ciric type mappings in the setup of partially ordered spaces. Moreover, the T -generalized weakly contractive mappings are introduced and also sufficient conditions for obtaining fixed points of such mappings in ordered spaces are studied. As an application of our results, periodic points of T -Banach operators are obtained. Finally, we provide some examples to illustrate the results presented herein.

Abstract. The refined direct and inverse estimates for -derivatives of functions in weighted variable exponent Lebesgue spaces are proved.

Abstract. Using the inverse system approach of continuous maps, in this paper we study the (co)homological properties of continuous maps. Applications of the obtained results include the constructions of long exact sequences of continuous maps for homology pro-groups, cohomology inj-groups, Čech homology groups and Čech cohomology groups.

Abstract. In this paper the method of Löwner chains is used to establish some sufficient conditions for the univalence of analytic functions defined in the punctured unit disk . Also we refine a quasiconformal extension criterion with the help of Becker's method. A number of univalent conditions would follow upon specializing the parameters involved in our main results.

Abstract. In this paper, we discuss the semicontinuities of the orbital and limit set maps, and investigate their relationships with the stabilities of orbits. First we prove that if a point is positively Zhukovskij stable, then the limit set maps are upper semicontinuous at that point. Then we show that if the limit sets of a point are stable (or eventually stable or uniformly eventually stable), then the corresponding limit set maps are upper semicontinuous at that point. Furthermore, we give several sufficient conditions to guarantee that the limit set maps are lower semicontinuous.

Abstract. In this paper we demonstrate that in many cases the investigation of the problem of controlling chaos, which is of great theoretical and practical importance, can be reduced to the stability analysis of the corresponding integro-differential equations. We consider stabilization for the configuration of a magneto-elastic beam and a two magnet system known as “Moon's beam”. Then we study an unstable system, in which the Lorenz attractor appears, and stabilize it by a control in integral form. In order to obtain stability results, we propose a special technique which is based on the idea of reduction of integro-differential equations to systems of ordinary differential equations.

Abstract. Let T denote the interval . In this paper, some theorems for approximation by trigonometric polynomials in the Orlicz space are proved. Under certain conditions, we prove the existence of derivatives of functions belonging to the Orlicz space and investigate the approximation properties of the derivatives of trigonometric polynomials. Note that the estimate obtained between the derivatives of functions and the derivatives of trigonometric polynomials depends on a sequence of best approximations in the Orlicz space .

Abstract. Some topologic-geometrical properties of external bisectors of a triangle are studied by a weak form of the completeness axiom. The case of non-isosceles triangles with two congruent external bisectors is given special.

Abstract. In this paper we deal with real oscillatory functions of the form where , as and is periodic. We impose some sufficient conditions on functions and S which imply the d -dimensional fractal oscillatority of the function with , thus extending a result of Tricot (1995). Using the obtained results, we show that the oscillatory dimension of both component functions of the p -clothoid is equal to , where , and that the corresponding reflected functions are d -dimensional fractal oscillatory. The case where was treated previously by Korkut et al. (2008, 2009)

Abstract. In the present paper, we give the concrete representation in terms of a space of functions for the tensor products of the weighted Lorentz spaces Λ G p,q ( w ) and get the space of multipliers from the Lorentz space to the Lorentz space or , in particular, to , where and . The methods used in the paper are based on the application of weights .

Abstract. P. Tchamitchian has constructed an atomic decomposition of the real Hardy space with L p -atoms () by rearrangements of wavelet expansion. In this paper, we give a characterization of Triebel–Lizorkin spaces and Besov spaces by a BMO family expansion by applying the arguments above.

Abstract. In the paper, the class is established, to which a majorant function belongs when the initial function belongs to the space . Integral representations of functions of the space are found when . The multipliers of inclusion from the space to the spaces H 2 , H 1 and are defined.