شماره کتابشناسی ملی
شماره
۲۰۳۳۲پ
زبان اثر
زبان متن نوشتاري يا گفتاري و مانند آن
per
عنوان و نام پديدآور
عنوان اصلي
نتایج در قضایای نقطه ثابت با متر برگمن و مسائل شکافت شدنی
عنوان اصلي به زبان ديگر
Some results in fixed point theorems with Bregman distance and split feasibility problems
نام نخستين پديدآور
/معصومه رئیسی شندی
وضعیت نشر و پخش و غیره
نام ناشر، پخش کننده و غيره
: علوم ریاضی
تاریخ نشرو بخش و غیره
، ۱۳۹۷
نام توليد کننده
، راشدی
مشخصات ظاهری
نام خاص و کميت اثر
۱۲۴ص
یادداشتهای مربوط به نشر، بخش و غیره
متن يادداشت
چاپی - الکترونیکی
یادداشتهای مربوط به پایان نامه ها
جزئيات پايان نامه و نوع درجه آن
دکتری
نظم درجات
ریاضی محض
زمان اعطا مدرک
۱۳۹۷/۰۶/۱۳
کسي که مدرک را اعطا کرده
تبریز
یادداشتهای مربوط به خلاصه یا چکیده
متن يادداشت
Nonlinear analysis deals with the study of nonlinear mappings between vector spaces (or subsets of them). But the general idea is that not only maps but also spaces can be nonlinear. Many nonlinear analysis problems such as Convex Analysis, Variational Analysis, Optimization, Monotone Mapping Theory and Differential Equations, can be formulated in the form of the fixed point problem. There are many ways to solve this problem in Hilbert spaces and uniformly convex and uniformly smooth Banach spaces. When we are going to extend these methods to the general reflexive Banach spaces, we encounter some difficulties because many of the useful examples of nonexpansive operators in Hilbert spaces are no longer firmly nonexpansive or even nonexpansive in Banach spaces. There are several ways to overcome these difficulties, one of which is the use of Bregman distance instead of norm. Therefore, the defininitions of types of nonexpansive mappings will be defined with respect to the Bregman distance instead of with respect to the norm. These definitions are useful in the setting of Banach spaces since we have several examples of operators satisfying them. In addition, if we go back to Hilbert spaces and take these new definitions with respect to the function f(x) = 1 2x2, then they coincide with the usual definitions. In this thesis, we introduce new iterative methods for solving various optimization problems in reflexive Banach spaces. In this direction, we present some algorithms for the approximation of fixed points of some types of nonexpansive mappings, the zero set of monotone mappings,the solution set of equilibrium problems with respect to pseudomonotone mappings and the solution set of SCNP, SCFP, MSSFP Problems. Monotone operators have an important role in nonlinear analysis and finding the zero set of these operators has particular importance. The fourth chapter is devoted to a detailed study of the problem of finding zeros of monotone operators in Hadamard spaces. In this chapter, we construct iterative methods such that the sequences generated by these methods converge to a common zero of monotone operators. Also some applications and numerical examples of proposed algorithms are presented
عنوان اصلی به زبان دیگر
عنوان اصلي به زبان ديگر
Some results in fixed point theorems with Bregman distance and split feasibility problems
نام شخص به منزله سر شناسه - (مسئولیت معنوی درجه اول )
مستند نام اشخاص تاييد نشده
رئیسی شندی، معصومه
مستند نام اشخاص تاييد نشده
Raeisi Shendi, Masoumeh
دسترسی و محل الکترونیکی
يادداشت عمومي
سیاه و سفید
وضعیت فهرست نویسی
وضعیت فهرست نویسی
نمایه‌سازی قبلی
