This paper aims at deriving and proving some Lipschitzian type error bounds for convex conic problems in a simple way First it is shown that if the recession directions satisfy Slater s condition then a global Lipschitzian type error bound holds Alternatively if the feasible region is bounded then the ordinary Slater condition guarantees a global Lipschitzian type error bound These can be consi...

In this paper we study the Plateau problem for affine maximal hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. In particular we formulate the affine Plateau problem as a geometric variational problem for the affine area functional, and we prove the existence and regularity of maximizers. As a special case, we obtain corresponding exist...

Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many orders of magnitude weaker than classical Airy ring intensities. Pupil mapping is therefore a candidate technique for coronagraphic imaging of extrasolar planet...

Teichmüller's problem from 1944 is this: Given \(x\in [0,1)\) find and describe the extremal quasiconformal map \(f\colon\mathbb{D}\to\mathbb{D}\), \(f|\partial \mathbb{D}=\) identity \(f(0)=-x\leq 0\). We consider this in setting of minimisers \(L^p\)-mean distortion. The classical result that there an Teichmüller type with associated holomorphic quadratic differential having a pole order one ...

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually vi...

We shall prove the equivalence bewteen the convergences of Mann and implicit Mann iterations dealing with various classes of non-Lipschitzian operators.

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.

In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. 2006 . In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings sat...

An explicit expression in terms of these parameters is obtained for AP. The fact that the integral in (3) remains bounded for 0^p<l under the assumption that C has continuously turning tangents was proved in an earlier paper of the writer [4, p. 362 j.1 The emphasis in the present note is upon the fact that the constant Ap depends only on the parameters indicated and is expressed explicitly in ...