A minimization theorem in quasi-metric spaces and its applications.

Ume, Jeong Sheok

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Extensions of minimization theorems and fixed point theorems on a quasimetric space.

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A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.

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