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Fixed point under general contraction conditions in G-metric space. (English) Zbl 1379.54036

Summary: Fixed point theorems are established under three types of general contraction conditions in a \(G\)-metric space \((X,G)\): one is of Nesic-type and two of twice-power contraction type. Further, the fixed point \(p\) obtained for a twice-power contraction \(f\) will be a \(G\)-contractive fixed point, in the sense that for each \(x_0\in X\), the \(f\)-iterates \(x_0, fx_0, f^2x_0,\dots\) converge to \(p\) in \(X\).

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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