Fixed point theorems and tiling problems
Copyright policy )Fixed point theorems and tiling problems
Let (X,d) be a complete metric space and let f : X ? X satisfy inf{?(x,y)d( fm(x), fm(y)) : m ? J}? Kd(x,y) for all x,y ? X and some K ? (0,1) and ? : X x X ? [0,?), where J is a set of positive integers. In this paper, we prove fixed point theorems for this mapping f. We also discuss the connection with tiling problems and give a titling proof of a fixed point theorem.
periodic point, Fixed-point theorems, fixed point, Fixed-point and coincidence theorems (topological aspects), Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., \(\alpha\)-\(k\)-contraction, good collection of tiles
periodic point, Fixed-point theorems, fixed point, Fixed-point and coincidence theorems (topological aspects), Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., \(\alpha\)-\(k\)-contraction, good collection of tiles
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