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...

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.