Abstract
Let X be a convex metric space with the property that even decreasing sequence of nonempty closed subsets of X with diameters tending to zero has nonempty intersection This paper proved that if T is a mapping of a closed convex nonempty subset K of X into itself satisfying the inequality: d(Tx, Ty)⩽ad(x, y)+b{d(x, Tx)+d(y, T y )} +c{d(x, Ty)+d(y, Tx)} for all x, y in K, where 0⩽a<1, b⩾0, c⩾0, a+c≠0 and a+2b+3c⩽1, then T has a unique fixed point in K.
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Communicated by Zhang Shi-sheng
The author is grateful to Professor Zhang Shi-seng of Sichuan University for his care and help in completion of this paper.
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Bing-you, L. Fixed point theorem of nonexpansive mappings in convex metric spaces. Appl Math Mech 10, 183–188 (1989). https://doi.org/10.1007/BF02014826
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DOI: https://doi.org/10.1007/BF02014826