Common Fixed Point Theorems for Six Mappings in Generalized Metric Spaces
نویسندگان
چکیده
and Applied Analysis 3 Definition 1.11 see 4 . Let f and g be two self-mappings from a G-metric space X,G into itself. Then the mappings f and g are said to be weakly compatible if G fgx, gfx, gfx 0 whenever G fx, gx, gx 0. Proposition 1.12 see 1 . Let X,G be a G-metric space. Then, for all x, y, z, a in X, it follows that i if G x, x, y 0, then x y z; ii G x, y, z ≤ G x, x, y G x, x, z ; iii G x, y, y ≤ 2G y, x, x ; iv G x, y, z ≤ G x, a, z G a, y, z ; v G x, y, z ≤ 2/3 G x, y, a G x, a, z G a, y, z ; vi G x, y, z ≤ G x, a, a G y, a, a G z, a, a . 2. Common Fixed Point Theorems Theorem 2.1. Let X,G be a complete G-metric space, and let f , g, h, A, B, and C be six mappings of X into itself satisfying the following conditions: i f X ⊂ B X , g X ⊂ C X , h X ⊂ A X ; ii for all x, y, z ∈ X, G ( fx, gy, hz ) ≤ kmax ⎧ ⎨ ⎩ G ( Ax, gy, gy ) G ( By, fx, fx ) , G ( By, hz, hz ) G ( Cz, gy, gy ) , G ( Cz, fx, fx ) G Ax, hz, hz ⎫ ⎬
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