We prove new norm equalities and inequalities for general n × n tridiagonal and antitridiagonal operator matrices, including pinching type inequalities for weakly unitarily invariant norms.
In this paper, we examine a nonlinear hyperbolic equation with a nonlinear integral condition. In particular, we prove the existence and the uniqueness of the linear problem by the Fadeo Galerkin method, and by applying an iterative process to some significant results obtained for the linear problem, the existence and the uniqueness of the weak solution for the nonlinear problem are additionally examined.
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