‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

In this paper we prove analogs of Korovkin’s theorem in the context weakly nonlinear and monotone operators acting on Banach lattices functions several variables. Our results concern convergence almost everywhere, measure $$L^{p}$$ -norm. Several illustrating theory are also included.

From recent studies, the concept of “monotone expectation” (ME) Interactive Multi-Attribute Decision Making (MADM) is well known, which was developed for case different fuzzy sets. This article develops such statistical parameters as variance, k-order moment and covariance. We investigate problem definition some parameters, when uncertainty represented by a monotone measure—a measure—instead an...

We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.

In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-s...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

We identify conditions for separating signaling equilibria where attributes are randomly related to costs. Under discrete attributes, a necessary and sufficient condition is the ordering of the cost distributions conditional on attributes by the Monotone Likelihood Ratio Property (MLRP). An equivalent condition is the monotone ordering of the cost elasticities of these distributions. Under a co...

In their seminal work which initiated random graph theory Erd os and R enyi discovered that many graph properties have sharp thresholds as the number of vertices tends to in nity We prove a conjecture of Linial that every monotone graph property has a sharp threshold This follows from the following theorem Let Vn p f g denote the Hamming space endowed with the probability measure p de ned by p ...

Many AI/Machine learning problems require adaptively selecting a sequence of items, each selected item might provide some feedback that is valuable for making better selections in the future, with goal maximizing an adaptive submodular function. Most existing studies this field focus on either monotone case or non-monotone case. Specifically, if utility function and submodular, Golovin Krause (...

We develop an algorithm for simulating \perfect" random samples from the invariant measure of a Harris recurrent Markov chain. The method uses backward coupling of embedded regeneration times, and works most eeectively for nite chains and for stochas-tically monotone chains even on continuous spaces, where paths may be sandwiched below \upper" and \lower" processes. Examples show that more naiv...