We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant Λ. If r denotes the area radius, m_g and q the gravitational mass and charge of a sphere with area radius r respectively, we find that for any solution which satisfies the condition p+2p_≤ρ, where p≥ 0 and p_ are the radial and tangential pressures respectively, ρ≥ 0 is the energy density, and for which 0≤q^2/r^2+Λ r^2≤ 1, the inequality m_g/r≤ 2/9+q^2/3r^2-Λ

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... /9√(1+3q^2/r^2+3Λ r^2) holds. We also investigate the issue of sharpness, and we show that the inequality is sharp in a few cases but generally this question is open.