Question
Let (X,D,K) be a complete metric-type space. Let f.g.S,T:X-X be given continuous mappings satisfying: if there exists a non-negative number a < such that for
Let (X,D,K) be a complete metric-type space. Let f.g.S,T:X-X be given continuous mappings satisfying: if there exists a non-negative number a < such that for each X, yeX D,8)=a max D(Sx,7y), D(x, S), DTy.8)D(S, g) + D(S,TY) such that S and T commute with fand g, respectively. Further let f(X)ET(X),. g(X)ES(X). Then show that f.g,S and T have a unique common fixed point.
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Calculus
Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon
9th edition
131429248, 978-0131429246
