Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

Abstract The invariant Galton–Watson (IGW) tree measures are a one-parameter family of critical with respect to large class reduction operations. Such operations include the generalized dynamical pruning (also known as hereditary in real setting) that eliminates descendant subtrees according value an arbitrary subtree function is monotone nondecreasing isometry-induced partial order. We show th...

We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.

Jensen–Steffensen type inequalities for P -convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen–Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

Technique of image reconstruction using Ftransform uses basic functions for computation. Radius and partition of these functions affects quality of the reconstruction. In this article we are focusing on influence of the basic function shape on the quality of reconstruction and providing results of nondecreasing, nonincreasing and oscillating examples.

We consider the scalar equation ẋ(t)+ m ∑ j=1 aj(t) ∫ h 0 x(t − s)dr j(s) = 0 (h = const > 0, ẋ = dx/dt), where r j(s) are nondecreasing functions. Besides, we do not require that aj(t) are positive for all t 0 . So the function z+ m ∑ j=1 aj(t) ∫ h

If the first lower symmetric derívate of a continuous function is nonnegative, then it is nondecreasing. If the second lower symmetric derívate of a continuous function is nonnegative, then it is convex. In this paper it is shown that if continuity is replaced by Baire one, Darboux in each of these, then the resulting statements are true.

This paper studies the global output convergence of a class of recurrent neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying inputs. We establish two sufficient conditions for global output convergence of this class of neural networks. Symmetry in the connection weight matrix is not required in the pres...

We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.