Error Bound for Conic Inequality in Hilbert Spaces

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

$G$-Frames for operators in Hilbert spaces

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

A refined Jensen's inequality in Hilbert spaces and empirical approximations

Let f : X→ R be a convex mapping and X a Hilbert space. In this paper we prove the following refinement of Jensen’s inequality: E(f |X ∈ A) ≥ E(f |X ∈ B ) for every A,B such that E(X |X ∈ A) = E(X |X ∈ B ) and B ⊂ A. Expectations of Hilbert space valued random elements are defined by means of the Pettis integrals. Our result generalizes a result of Karlin and Novikov (1963), who derived it for ...

Generalized Frames in Hilbert Spaces

Error bound results for convex inequality systems via conjugate duality

The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of...