Functions with bounded variation in locally convex space

Minimizing Convex Functions with Bounded Perturbations

When a convex function f : D → R is disturbed by some nonlinear bounded perturbation p : D → R, the arising function f̃ = f + p is no more convex and its local minimizers are no more global minimizers. In order to get some similar properties for f̃ , we use a convexity modulus of f named h1 and its generalized inverse function h−1 1 , and show that f̃ is outer γ-convex for any γ ≥ γ∗ := h−1 1 ( 2 ...

Strongly almost ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

Harmonic functions in non-locally convex spaces

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.

Minimizing functions with bounded variation of subgradients

In many applications it is possible to justify a reasonable bound for possible variation of subgradients of objective function rather than for their uniform magnitude. In this paper we develop a new class of efficient primal-dual subgradient schemes for such problem classes.