‎In this work four uncertain delay differential equations of Volterra-Levin type will be considered‎. ‎Applying suitable contraction mapping and fixed point method‎, ‎the stability the studied‎. ‎It shown that solutions are bounded and‎, ‎with additional condition‎, tend to zero‎. ‎Also‎, ‎a necessary sufficient condition for asymptotic an equation presented‎.

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance can be finite-, high-, or infinite-dimensional. A mixture point masses at zero and continuous distributions is used the prior distribution on coefficients, appropriate parameters. The optimal posterior contraction hampered by p...

In this paper, we introduce the concept of contractive pair maps and give some necessary sufficient conditions for existence uniqueness best proximity points such pairs. our approach, have been weakened. An application has presented to demonstrate usability results. Also, cyclic ?-contraction asymptotic convergence theorems on point mappings. The results extend, generalize improve known from th...

We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all root-key distances or over all root-node distances) in random m-ary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when 3 6 m 6 13 but becomes of higher order when m > 14. Surprisingly, the corresponding asymptotic correl...

Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite the Riemannian metric. In infinite-dimensional setting, however, such analysis generally restricted to norm-contracting systems. We develop a generalization of geodesic rates Banach spaces using smoothly-weighted semi-inner product structure on tangent s...

Abstract We consider the propagation of stratified fluid through a contraction near resonance, for which the governing asymptotic equation is the forced KdV equation. Steady solutions of this equation are sought which have constant, but differing amplitudes upstream and downstream of the contraction, and for which leading order dispersive effects are retained. A numerical algorithm is outlined ...

In many iterative optimization methods, fixed-point theory enables the analysis of convergence rate via contraction factor associated with linear approximation operator. While this characterizes asymptotic convergence, it does not explain non-linear behavior these algorithms in non-asymptotic regime. letter, we take into account effect first-order error and present a closed-form bound on terms ...