کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8899624 | 1631549 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Normal structure and orbital fixed point conditions
ترجمه فارسی عنوان
ساختار عادی و شرایط نقطه ثابت مداری
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کلمات کلیدی
ساختار عادی، نقشه برداری غیرقابل انعطاف نقاط ثابت، قطر مداری کاهش می یابد، نقشه برداری غیر ارگانیک، نقشه برداری انقباضی،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
In some sense all of the results discussed in this paper are an outgrowth of the concept of 'normal structure' introduced by Brodskii and Milman in 1948 and following related idea introduced by Belluce and Kirk in 1969. A mapping T of a metric space K into itself is said to have 'diminishing orbital diameters' if given any xâK it is the case thatlimnâââ¡diam(O(Tn(x)))0, where O(x)={x,T(x),T2(x),â
â
â
}. Among other things Belluce and Kirk observed that the assumption of diminishing orbital diameters on a mapping T:KâK is sufficient to assure that T has a fixed point if T is nonexpansive and if K is a weakly compact convex subset of a Banach space. It was later shown by Kirk that the convexity assumption on K can be dropped. The purpose of this discussion is to illustrate how the above ideas are related to a number of similar ones that have been introduced more recently. Among these is the following concept introduced recently by Amini-Harandi, et al. A mapping T:KâK of a subset K of a Banach space is said to be nonexpansive wrt orbits if for all x,yâK,âT(x)âT(y)ââ¤rx(O(y)) whererx(O(y))=supâ¡{âxâuâ:uâO(y)}. It is shown that if K is a weakly compact subset of a Banach space and if T:KâK is nonexpansive wrt orbits then the following condition always assures the existence of a fixed point for T: For each xâK with T(x)â x,infmâNâ¡{limâ¡supnâââ¡âTm(x)âTn(x)â}
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 463, Issue 2, 15 July 2018, Pages 461-476
Journal: Journal of Mathematical Analysis and Applications - Volume 463, Issue 2, 15 July 2018, Pages 461-476
نویسندگان
W.A. Kirk, Naseer Shahzad,