We determine and estimate the Ptolemy constant of absolute normalized norms on ℝ 2 by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject Classification: 46B20.
Abstract. In this paper we consider the convergence of iterative processes for a family of multivalued nonexpansive mappings. Under somewhat different conditions the sequences of Noor, Mann and Ishikawa iterates converge to the common fixed point of the family of multivalued nonexpansive mappings.Mathematics subject classification (2010): 47H09, 47H10, 47H15..
We define a mean nonexpansive mappingTonXin the sense thatTx-Ty≤ax-y+bx-Ty,a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness theorems of fixed point.
Abstract. We show some geometric conditions on a Banach space X concerning the generalized James constant, the generalized Jordan-von Neumann constant, the generalized Zbagȃnu constant and the coefficient R(1,X) , which imply the existence of fixed points for multivalued nonexpansive mappings. Our results extend and improve some recent results.Mathematics subject classification (2010): Primary 47H10, Secondary 46B20.
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