Fixed Point Theorems in Cone Banach Spaces
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2009
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Springer international Publishing Ag
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Abstract
In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm parallel to x parallel to(P) = d(x, 0), if there exist a, b, s and T : C -> C satisfies the conditions 0 <= s + vertical bar a vertical bar - 2b < 2(a + b) and 4ad(Tx, Ty) + b(d(x, Tx) + d(y, Ty)) <= sd(x, y) for all x, y is an element of C, then T has at least one Fixed point. Copyright (C) 2009 Erdal Karapinar.
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KARAPINAR, ERDAL/0000-0002-6798-3254
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