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Stability results for Jungck-type iterative processes in convex metric spaces. (English) Zbl 1293.54033
Let $$(E, d)$$ be a complete convex metric space in the sense of W. Takahashi [Kodai Math. Semin. Rep. 22, 142–149 (1970; Zbl 0268.54048)] and $$Y$$ a nonempty closed convex subset of $$E$$. Following the reviewer, C. Bhatnagar and S. N. Mishra [Int. J. Math. Math. Sci. 2005, No. 19, 3035–3043 (2005; Zbl 1117.26005)], the authors obtain stability results for Jungck-Mann and Jungck-Ishikawa iterations for a pair of nonself mappings $$S, T: Y \to E$$ satisfying the conditions $$T(Y)\subseteq S(Y)$$, $$S(Y)$$ is a complete subspace of $$E$$, and $$d(Tx, Ty)\leq \delta d(Sx,Sy) + Lu(x, y)$$, where $$0\leq\delta<1$$, $$L\geq 0$$ and $$u(x, y) = \min\{d(Sx,Tx), d(Sy, Ty), d(Sx, Ty), d(Sy, Tx),\frac{1}{2}[d(Sx,Tx)+d(Sy,Ty)], \frac{1}{2}[d(Sx,Ty)+d(Sy,Tx)] \}.$$

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47J25 Iterative procedures involving nonlinear operators
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##### References:
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