It is proved that in an idealized uniform probabilistic model the cost of a partial match query in a multidimensional quadtree after normalization converges in distribution. The limiting distribution is given as a fixed point of a random affine operator. Also a first-order asymptotic expansion for the variance of the cost is derived and results on exponential moments are given. The analysis is ...

*Correspondence: [email protected] Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran Abstract In this paper, we study some fixed point theorems for self-mappings satisfying certain contraction principles on a convex complete metric space. In addition, we investigate some common fixed point theorems for a Banach operator pair under certain generalized contractions on a convex c...

In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. Schauder’s fixed point Theorem is the main tool used here to establish the existence ...

For ill-posed linear operator equations we consider some V-cycle multigrid approaches, that, in the framework of Bramble, Pasciak, Wang, and Xu (1991), we prove to yield level independent contraction factor estimates. Consequently, we can incorporate these multigrid operators in a full multigrid method, that, together with a discrepancy principle, is shown to act as an iterative regularization ...

Correspondence: [email protected] Department of Elementary Education, Heze University, Heze 274000, Shandong, People’s Republic of China Abstract By obtaining intervals of the parameter l, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. ...

We apply a method developed by one of the authors, see [1], to localize the numerical range of quasi-sectorial contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups {exp(−tS)}t≥0, and the maximal sectorial generators S. We also give a new prove of the rate O(1/n) for the operator-norm Euler formula approximation: e...

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, w...

For an $$n\times n$$ complex matrix C, the C-numerical range of a bounded linear operator T acting on Hilbert space dimension at least n is set numbers $$\textrm{tr}\,(CX\,^*\,TX)$$ , where X partial isometry satisfying $$X^*X = I_n$$ . It shown that $$\begin{aligned} \textbf{cl}(W_C(T)) \cap \{\textbf{cl}(W_C(U)): U \hbox { unitary dilation } T\} \end{aligned}$$ for any contraction if and only...

In the field of biological control, there are a large number systems that gradually evolve over certain period time. However, due to some natural or human intervention behavior, system state will be subjected relatively short time interference, so changes in an instant. This sudden change makes not simply described by continuous discrete dynamical systems, but means impulse systems. this paper,...