We consider the nonlocal boundary value problem for difference equations (iik - Uk~i)/r + Auk = 9/c, 1 < /c < IV, N'T = 1, and UQ = U[/x + , 0 < A < 1, in an arbitrary Banach space E with the strongly positive operator A. The well-posedness of this nonlocal boundary value problem for difference equations in various Banach spaces is studied. In applications, the stability and coercive stability estimates in Holder norms for the solutions of the difference scheme of the mixed-type boundary value problems for the parabolic equations are obtained. Some results of numerical experiments are given.
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