Some new Lyapunov type theorems for stochastic difference equations with continuous time are proven. It is shown that these theorems simplify an application of Lyapunov functionals construction method.

Abstract An approximation, in the sense of $$\Gamma $$ Γ -convergence and any dimension $$d\ge 1$$ d ≥ 1 , Griffith-type functionals, with p -growth ( $$p>1$$ p > ) symmetrized gradient, is provid...

We introduce a typed programming formalism, type-2 inflationary tiered loop programs or ITLP2, that characterizes the type-2 basic feasible functionals. ITLP2 is based on Bellantoni and Cook’s [BC92] and Leivant’s [Lei95] type-theoretic characterization of polynomial-time and turns out to be closely related to Kapron and Cook’s [KC91, KC96] machine-based characterization of the type-2 basic fea...

Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as h -convex functions. In this paper, we aim to establish functional form of inequalities presented by prove superadditivity monotonicity properties these functionals. Furthermore, de...