۲۰۳۳۲پ
per
نتایج در قضایای نقطه ثابت با متر برگمن و مسائل شکافت شدنی
Some results in fixed point theorems with Bregman distance and split feasibility problems
/معصومه رئیسی شندی
: علوم ریاضی
، ۱۳۹۷
، راشدی
۱۲۴ص
چاپی - الکترونیکی
دکتری
ریاضی محض
۱۳۹۷/۰۶/۱۳
تبریز
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
Some results in fixed point theorems with Bregman distance and split feasibility problems
رئیسی شندی، معصومه
Raeisi Shendi, Masoumeh
سیاه و سفید
نمایهسازی قبلی
