Theorem 2. Picard-Lindelof existence/uniqueness theorem Suppose f : (I × U) ⊆ (R × R) → R is continuous in (t, y) and uniformly Lipschitz in y. Then ∀(τ, ξ) ∈ (I × U), the ODE [ẏ = f(t, y) with y(τ) = ξ] has a unique solution on {t ∈ I : |t− τ | < α} for some α > 0. Depends on: Completeness of R, Gronwalls lemma (for uniqueness Proof idea: 5 steps: 1. Choose a, b s.t. {t : |t − τ | < a} ⊆ I and...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

in order to estimate the effects of the macrc~econornic indicators on the income distribution of iran, the time series data during the period of 1971-1991 were used. first the yammetric inequality indicators (the gini coefficients) were estimated for the years 1991-1972. the results show the lowest level of inequality in 1980 with g=0.42 and the highest level in 1982 with g=0.55. arzulysing the...

equitable distribution of income and economic growth are challenges for policy-makers. therefore, it is important to investigate the influencing factors of it. given that financial development is an important factor affecting on income inequality, in this study, the effect of financial development on the gini coefficient as income inequality index is examined with using panel data methods durin...