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and Applied Analysis 3 for every x, y ∈ X and every Cauchy sequence of the form {TSnx} for x ∈ X converges in X. Then i d TS, TS ≤ qδ O Tx, n , for all i, j ∈ {1, 2, . . . , n}, for all x ∈ X and n ∈ N, ii δ O Tx,∞ ≤ 1/ 1 − q d Tx, TSx , for all x ∈ X, iii S has a unique fixed point b ∈ X, iv lim TSx Tb. Proof. We will mainly follow the arguments in the(More)
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