A Qk(R ) -valued function is essentially a rule assigning k unordered and non necessarily distinct elements of R to each element of its domain set A ⊆ R . For a Qk(R) valued function f we construct a decomposition into k branches that naturally inherit the regularity properties of f . Next we prove that a measurable Qk(R ) -valued function admits a decomposition into k measurable branches. An e...

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend

Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation (Lipschitzian or monotonic) are given. Applications in relation with the well-known Čebyšev, Grüss, Ostrowski and Lupaş inequalities are provided as well.

In this article, we consider the H?lder continuity of injective maps in Orlicz-Sobolev classes defined on unit ball. Under certain conditions growth dilatations, obtain indicated class mappings. particular, under special restrictions, show that Lipschitz mappings holds. We also and harmonic particular classes. addition planar case, some situations map is bi-Lipschitzian if Beltrami coefficient ...

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variati01~al analysis and its applications, especially for issues related to variational stability and optimizatiou. \Ve develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative ...