Advances in Analysis

8

Authors: K.P.R. Rao, A.Som Babu, Md.Mustaq Ali

In this paper, we obtain a Presic type fixed point theorem for two pairs of jointly 2k-weakly compatible maps in fuzzy metric spaces.We also give an example to illustrate our main theorem. We obtain two corollaries for three maps and two maps.

10

Authors: Adela Ionescu, Mario Lefebvre, Florian Munteanu

Using the feedback linearization method, a state feedback control for the two-dimensional Kermack-McKendrick model for the spread of epidemics is obtained. This form of the dynamical system is suitable to carry out a qualitative analysis of the model. An optimal control problem for a stochastic version of the model is also set up and solved explicitly in a particular instance.

29

Authors: V.S. Guliyev, E.J. Ibrahimov, S.Ar. Jafarova

In this paper we consider some problems of the theory of approximation of functions on interval [0, ∞) in the metric of Lp,λ with weight sh2λ x using generalized Gegenbauer shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Gegenbauer shifts. We establish the equivalence of the modulus of smoothness and K-functional, defined in terms of the space of the Sobolev type corresponding to the Gegenbauer differential operator. We define function spaces of Nikol’skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use some functions classes of spectrum. In these classes, we prove analogues of Bernstein’s inequality and others for the Gegenbauer differential operator. Our results are analogues of the results for generalized Bessel shifts obtained in the work [30].