Class of spherically symmetric Stephani cosmological models is examined in the context of evolution type. It is assumed that the equation of state at the symmetry center of the models is barotropic (p(t) = αρ(t)) and the function k(t) playing role of spatial curvature is proportional to Stephani version of the Friedmann-Robertson-Lemaitre-Walker scale factor R(t) (k(t) = βR(t)).Classification of cosmological models is performed depending on different values and signs of parameters α and β. It is shown that for β < 0 (hyperbolic geometry) dust-like (α = 0) cosmological model exhibits accelerated expansion at later stages of evolution.The Hubble and deceleration parameters are defined in the model and it is shown that the deceleration parameter decreases with the distance becoming negative for sufficiently distant galaxies.Redshift-magnitude relation m(z) is calculated and discussed in the context of SnIa observational data. It is noticed that the most distant supernovae of type Ia fit quite well to the relation m(z) calculated in the considered model (H 0 = 65 km/sMpc, Ω 0 ≤ 0.3) without introducing the cosmological constant.It is also shown that the age of the universe in the model is longer than in the Friedmann model corresponding to the same H 0 and Ω 0 parameters.PACS numbers: 98.62. Py, 98.80.Es, 98.80.Hw 1

Spherically symmetric Stephani cosmological models are considered in the context of angular sizes of compact as well as expanding objects percepted by an observer placed at the symmetry centre. We assume that the matter filling up Stephani universe satisfies barotropic equation of state at the symmetry centre p(r ≈ 0, t) = αρ(t). Angular sizes of compact objects are examined as a function of parameter α, of energy density parameter Ωα0 and of the redshift z. Small angle anisotropies of microwave background radiation connected with typical density fluctuation of mass corresponding to a galaxy are also calculated in the model. Finally the horizon problem is discussed in detail.