Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to continuity with respect to initial conditio...

Inspired by the concept of integral type (Branciari type) contractive condition and respective fixed point results, we derive some new common fixed point theorems for quadruple self mappings satisfying a generalized W -contractive condition or a generalized -contractive condition of integral type, also using the notions of compatibility and subsequential continuity (alternately subcompatibility...

In the paper [9] we introduced the class of generalized metric spaces. These spaces simultaneously generalize ‘standard’ metric spaces, probabilistic metric spaces and fuzzy metric spaces. We show that every generalized metric space is, naturally, a uniform space. Thus we can use standard topological techniques to study, for example, probabilistic metric spaces. We illustrate this by proving a ...

For a function f ∈ L2,γ (ℝ2), the q-averaging of generalized m-order modulus continuity Ωm,γ (f) with weight φ, i.e., value

In the present paper, we have studied the analogue of some continuous functions in generalized topological space and consequently their behavior in fine topological space (cf. [18]).