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We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation u t − ∆u = φ(t)f (x, y), t ∈ (0, T), (x, y) ∈ (0, 1) × (0, 1), u(x, y, T) = g(x, y) with a homogeneous Cauchy boundary condition, where φ and g are given approximately. The problem is severely ill-posed. Using an interpolation method and… (More)

We give a proof for a conjecture suggested by Olivier de La Grandville and Robert M. Solow, which says that the general mean of two positive numbers, as a function of its order, has one and only one inflection point.

We give a proof for a conjecture suggested by Olivier de La Grandville and Robert M. Solow, which says that the general mean of two positive numbers, as a function of its order, has one and only one inflection point.

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of different vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the… (More)

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