It is known that the subdifferential of a lower semicontinuous convex function f over a Banach space X determines this function up to an additive constant in the sense that another function of the same type g whose subdifferential coincides with that of f at every point is equal to f plus a constant, i.e., g = f + c for some real constant c. Recently, Thibault and Zagrodny introduced a large cl...

Abstract Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as fractional-order Sobolev spaces) operator-valued multiplication in terms the Laplace transform are considered. These objects closely related to input–output time-invariant control systems. Characterisations when such map continuously between certain i...

Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Assume that g is a real-valued convex function and the gradient ∇g is [Formula: see text]-ism with [Formula: see text]. Let [Formula: see text], [Formula: see text]. We prove that the sequence [Formula: see text] generated by the iterative algorithm [Formula: see text], [Formula: see text] converges strongly to [Formul...

Mathematics Institute Warwick University CV4 7AL, UK e-mail: [email protected] Abstract: Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying efficiency. In particular they facilitate precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to...

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a produ...

The problem of constructing a measure on discrete set X taking values in positive cone bounded operators Hilbert space is considered. It assumed that projectionvalued function defined subset X0 the original initially given. aim study to find such scalar μ and continuation projector-valued from X, which results an operator-valued having density relative μ. In general, solved for |X| = 4 |X0| 2. ...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

This article contains essentially a rewriting of several properties two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and 6 j symbol, usually irrational, in terms related integer-valued functions called gon tet. Existence these avatars, sharing most essential with their more popular partners, although known fact, often overlooked. The tet are easie...

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a produ...

Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in  the unit ball of  the Hilbert space. ...