The present paper is aimed at solving initial value problems by the contraction-mapping principle in case an interior estimate is true in the function space under consideration. reziume. naSr omis mizania saCKisi amocanis kumSviTi asaxvis prin-cipiT amoxsna im SemT xvevaSi, roca gansaxil vel sivr ceSi samar Tl iania pirvel i rigis Carmoebu l ebis SePaseba gansazG vr is aris SigniT mo-Tavsebu l ...

In the case of oscillatory potentials, new oscillation criteria are established for the forced nonlinear differential equations ` |x′(t)|αsgnx′(t) ́′ + q(t)|x(t)|sgnx(t) = g(t) (β > α > 0). (*) Our results generalize and improve the main result of Nasr [3] for equation (∗) with α = 1, β > 1 and can be applied to extreme cases such as R∞ t0 q(t)dt = −∞ and R∞ t0 g(t)dt = −∞.

In this paper, for the Stratified Median Ranked Set Sampling (SMRSS), proposed by Ibrahim et al. (2010), we examine the proportional and optimum sample allocations that are two well-known methods for sample allocation in stratified sampling. We show that the variances of the mean estimators of a symmetric population in SMRSS using optimum and proportional allocations to strata are smaller than ...