Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets.
Kaczor, Wiesława (2003)
Abstract and Applied Analysis
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Kaczor, Wiesława (2003)
Abstract and Applied Analysis
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Vijayaraju, P. (1994)
International Journal of Mathematics and Mathematical Sciences
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Eun Suk Kim, W. A. Kirk (2001)
Annales Polonici Mathematici
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Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions...
Ghosh, M.K., Debnath, L. (1997)
International Journal of Mathematics and Mathematical Sciences
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W. A. Kirk, Carlos Martinez-Yanez (1990)
Annales Polonici Mathematici
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Andrzej Wiśnicki (2012)
Fundamenta Mathematicae
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We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.
Kittipong Sitthikul, Satit Saejung (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.
Maiti, M., Saha, B. (1993)
International Journal of Mathematics and Mathematical Sciences
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Kaewcharoen, A., Kirk, W.A. (2006)
Fixed Point Theory and Applications [electronic only]
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A. Anthony Eldred, W. A. Kirk, P. Veeramani (2005)
Studia Mathematica
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The notion of proximal normal structure is introduced and used to study mappings that are "relatively nonexpansive" in the sense that they are defined on the union of two subsets A and B of a Banach space X and satisfy ∥ Tx-Ty∥ ≤ ∥ x-y∥ for all x ∈ A, y ∈ B. It is shown that if A and B are weakly compact and convex, and if the pair (A,B) has proximal normal structure, then a relatively nonexpansive mapping T: A ∪ B → A ∪ B satisfying (i) T(A) ⊆ B and T(B) ⊆ A, has a proximal point in...
Du, Wei-Shih, Huang, Young-Ye, Yen, Chi-Lin (2002)
International Journal of Mathematics and Mathematical Sciences
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W. Kirk, W. Ray (1979)
Studia Mathematica
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Liu, Guimei, Lei, Deng, Li, Shenghong (2000)
International Journal of Mathematics and Mathematical Sciences
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