We derive two upper bounds for the probability of deviation a vector-valued Lipschitz function collection random variables from its expected value. The resulting can be tighter than obtained by direct application classical theorem due to Bobkov and Götze.

This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Carathéodory conditions and certain monotonicity conditions.

In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Carathéodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.

We introduce one-sided Lipschitz (OSL) conditions of set-valued maps with respect to given set differences. The existence of selections of such maps that pass through any point of their graphs and inherit uniformly their OSL constants is studied. We show that the OSL property of a convex-valued set-valued map with respect to the Demyanov difference with a given constant is characterized by the ...

We use Baire categorical arguments to construct dramatically pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that \almost every continuous real-valued function deened on 0,1] is nowhere diierentiable". As with the results of Banach and Mazurkiewicz, it appears...