الگوریتم همگرای قوی برای حل یک مسئله تعادل و مسئله نقطه ثابت با استفاده از فاصله برگمن در فضاهای باناخ
الموضوعات :
مصطفی قدم پور
1
,
ابراهیم سوری
2
1 - گروه ریاضی، دانشکده علوم پایه، دانشگاه پیام نور، تهران، ایران
2 - گروه ریاضی، دانشکده علوم پایه، دانشگاه لرستان، خرم آباد، ایران
الکلمات المفتاحية: Bregman nonexpansive mapping, Variational inequality, Fixed point problem, Frechet differentiable, Asymptotical fixed point,
ملخص المقالة :
در این مقاله، با استفاده از فاصله برگمن، الگوریتم جدیدی از نوع تصویر برای یافتن یک عنصر مشترک از مجموعه جواب های یک مسئله تعادل و مجموعه ای از نقاط ثابت معرفی می کنیم. سپس همگرایی قوی دنباله تولید شده با الگوریتم در شرایط مناسب اثبات می گردد. در واقع ثابت می کنیم که دنباله تولید شده با این الگوریتم به تصویر یک نقطه روی اشتراک مجموعه نقاط ثابت و مجموعه جواب مسئله تعادل همگراست. برای این منظور یک شرط برگمن از نوع لیپ شیتس برای یک تابع دو متغیره شبه یکنوا معرفی می کنیم. در ادامه، به کاربردی از مسئله نابرابری تغییراتی می پردازیم و از نتایج خود برای تعیین یک نقطه مشترک از مجموعه جواب مسئله نابرابری تغییراتی و مجموعه نقاط ثابت نگاشت غیر انبساطی استفاده می کنیم. در پایان، با استفاده از نرم افزار متلب، یک مثال عددی برای نشان دادن عملکرد همگرایی الگوریتم اصلی ارائه می دهیم.
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