Some new inequalities are obtained relating to the generalized trapezoid and midpoint rules for the Riemann–Stieltjes integral with a convex integrand and monotone nondecreasing integrator. Results are deduced for the special case of weighted Riemann integrals. Mathematics subject classification (2000): Primary 26D15, Secondary 26D10..

We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions. The models and results are illustrated on a portfolio optimization problem.

We study subsets of [1, x] on which the Euler φ-function is monotone (nondecreasing or nonincreasing). For example, we show that for any > 0, every such subset has size < x, once x > x0( ). This confirms a conjecture of the second author.

An example is presented to show that the worst case complexity of Bertsekas small label rst strategy for the shortest path problem is exponential It becomes polynomial if when scanning a node i its successors j i are examined in the nondecreasing order of dij the distance between i and j

Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.

Consider a nondecreasing homeomorphisms f defined on [0, 1] such that $$f(x)<x $$ for all $$x\in ]0,1[$$ . In this paper, we provide necessary and sufficient conditions to be part of $${\mathcal {C}}$$ -hairpin concentrates the mass bivariate copula. addition, study when copulas kind come from modular functions. Finally, under certain conditions, give multidimensional method generalizes case al...

In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, obtain an approximation to uniformly functions through new operator. Furthermore, calculate error estimation of approach with modulus continuity The obtained results are supported by visualizing explicit example. Finally, investigate relation between operators ge...

In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that drift coefficient is unbounded, verifies a spatial linear growth condition and componentwise nondeacreasing. Our approach consists of showing result bounded nondecreasing using both local time-space representation law iterated logarithm sheets. The d...