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For a constant k ∈ 0, ∞) a normalized function f , analytic in the unit disk, is said to be k -uniformly convex if Re (1 + zf ″( z ) /f ′( z )) > k | zf ″( z )/ f ′( z )| at any point in the unit disk. The class of k -uniformly convex functions is denoted k - ucv (cf. Kanas,...
The paper presents recent results concerning the problem of the existence of those selections, which preserve the properties of a given set-valued mapping of one real variable taking on compact values from a metric space. The properties considered are the boundedness of Jordan, essential or...
We consider a motion of a viscous compressible heat conducting fluid of a fixed mass bounded by a free surface. For a local solution of equations describing such a motion we derive some energytype inequalities which are necessary to prove the global existence of solutions.
Let ( X n ) be a sequence of independent not necessarily identically distributed random vectors belonging to the domain of attraction of a stable or semistable hemigroup, i.e. for an increasing sampling sequence ( k n ) such that k n+1 / k n → c ≥ 1 and linear operators A n , the normalized...
In this paper, we investigate a class of hyperbolic differential equations of neutral type and obtain some new sufficient conditions of the oscillation for such equations satisfying boundary condition
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