γ—Lipschitz 模数与抽象 Volterra 积分方程

γ-LIPSCHITZ MODULI AND ABSTRACT VOLTERRA INTEGRAL EQUATIONS

本文中设 G 是具正则 Borel 测度 μ的局部紧 Hausdorff 空间.设已给定 G 的非空紧子集族{G_t:t∈G},它满足以下条件:(A_1)(?)μ(G_tΔG_s)=0,Δ记对称差;(A_2)s∈G_t(?)G_s(?)G_t;(A_3)存在 t_0∈G,使 (?)μG_t=0,且对 t_0的任何邻域 W,有 t_0的邻域 U。

In this paper,abstract Volterra integral equations.in Banach spaces of the formx(t)=u(t)+integral from G_(?) f(t,s,x(s)) ds,where {G_t} is a family of subsets of some locallycompact Hausdorff space G satisfying certain conditions are considered.By meansof the concept of γ-Lipschitz modulus of an operator and a certain fixed pointtheorem,some existence results for solutions of the equations in question areobtained.