توسیع چند قضیه ی نقطه ثابت مشترک به نگاشت های میانگینی غیرانبساطی
محورهای موضوعی : آمار
شهرام سعیدی
1
(گروه ریاضی، دانشکده علوم، دانشگاه کردستان، سنندج، ایران.)
جعفر باغنده
2
(گروه ریاضی، دانشگاه کردستان، سنندج، ایران)
کلید واژه: semi-topological semi-group action, mean non-expansive, almost periodic functions, fixed point,
چکیده مقاله :
در سال 1963، دمار نشان داد که هر خانواده ی جابجایی از نگاشت های غیرانبساطی از زیرمجموعه های ناتهی، محدب و فشرده از فضای باناخ دارای نقطه ثابت است. تاکاهاشی قضیه ی دمار را برای نیم گروه های میانگین پذیر گسسته گسترش داد. در سالهای اخیر تحقیقات فراوانی روی نظریه نقطه ثابت و نقطه ثابت مشترک برای نگاشت های غیرانبساطی انجام شده است. برای نیم گروه های نیم توپولوژیک (یعنی یک نیم گروه به همراه یک توپولوژی هاوسدورف به طوری که عمل ضرب آن به طور مجزا پیوسته باشد) لائو و ژنگ قضیه دمار را تحت شزایط کلیتر از جمله میانگین پذیری فضای توابع تقریباً متناوب و به طور ضعیف تقریباً متناوب بررسی کردند. در این مقاله، ما چند خاصیت نقطه ی ثابت را برای عمل نیم گروه های نیم توپولوژیک میانگینی غیرانبساطی روی زیرمجموعه ی ناتهی، محدب و فشرده ی ضعیف از فضای موضعاً محدب بررسی می کنیم و گسترشی از نتایج لائو و ژانگ ارائه خواهیم داد.
In 1969, DeMarr proved that a commuting family of non-expansive mappings on a nonempty convex compact subset of a Banach space has a fixed point. Takahashi extended DeMarr’s theorem to the case of discrete amenable semi-groups. In recent years, considerable research has been devoted to the theory of fixed points as well as common fixed points. In the case of semi-topological semi-groups (that is, a semi-group with a Hausdorff topology such that the multiplication is separately continuous), Lau and Zhang studied DeMarr’s theorem under more general conditions for example in the case of the amenability of the space of almost periodic functions as well as the space of weakly almost periodic functions. In this paper, we study several fixed point properties of the mean non-expansive semi-topological semi-groups acting on nonempty convex weakly compact subsets of a locally convex space as well as give extensions of the results of Lau and Zhang.
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