Minimizing functions with bounded variation of subgradients

On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.

p-Lambda-bounded variation

A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.

A companion of Ostrowski's inequality for functions of bounded variation and applications

A companion of Ostrowski's inequality for functions of bounded variation and applications are given.

Some Perturbed Inequalities of Ostrowski Type for Functions whose n-th Derivatives Are Bounded

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients