کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
844825 | 908619 | 2006 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The Domínguez–Lorenzo condition and multivalued nonexpansive mappings The Domínguez–Lorenzo condition and multivalued nonexpansive mappings](/preview/png/844825.png)
Let E be a nonempty bounded closed convex separable subset of a reflexive Banach space X which satisfies the Domínguez–Lorenzo condition, i.e., an inequality concerning the asymptotic radius of a sequence and the Chebyshev radius of its asymptotic center. We prove that a multivalued nonexpansive mapping T:E→2XT:E→2X which is compact convex valued and such that T(E)T(E) is bounded and satisfies an inwardness condition has a fixed point. As a consequence, we obtain a fixed-point theorem for multivalued nonexpansive mappings in uniformly nonsquare Banach spaces which satisfy the property WORTH, extending a known result for the case of nonexpansive single-valued mappings. We also prove a common fixed point theorem for two nonexpansive commuting mappings t:E→Et:E→E and T:E→KC(E)T:E→KC(E) (where KC(E)KC(E) denotes the class of all compact convex subsets of E) when X is a uniformly convex Banach space.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 64, Issue 5, 1 March 2006, Pages 958–970