18667

16212

كارشناسي ارشد

رياضيات و كاربردها

اصفهان : دانشگاه صنعتي اصفهان

1402

شش، 103 ص. : مصور، نمودار

1402/05/15

كتابنامه

رياضي

رياضي

1402/05/16

2948261

در اين پايان‌نامه، ابتدا شبكه‌ي باناخ را معرفي مي‌كنيم و به بيان ويژگي‌هاي آن مي‌پردازيم. سپس AM -‌فضا و AL -‌فضا را معرفي مي‌نماييم و نشان مي‌دهيم يك شبكه‌ي باناخ AM -‌فضا (AL -‌فضا) است اگر و تنها اگر دوگان آن AL -‌فضا (AM -‌فضا) باشد. همچنين وجود نقطه ثابت را براي نگاشت‌هاي ناانبساطي در اين فضاها بررسي مي‌نماييم و نشان مي‌دهيم تحت چه شرايطي مجموعه‌اي از تمام توابع اساساً كراندار و دوگان يك AL -‌فضا داراي نقطه ثابت باشند. در آخر، زيرمجموعه‌ي بسته، كراندار و محدب W از فضاي همه دنباله‌هاي همگرا در ميدان اعداد حقيقي را كه نافشرده در توپولوژي ضعيف باشد، چنان معرفي مي‌كنيم كه هر نگاشت ناانبساطي T: W →W داراي نقطه ثابت باشد.

Let X be a vector space. X is said to be an ordered vector space whenever it is equipped with an order relation ≥ (i.e., ≥ is a reflexive, anti symmetric and transitive binary relation on X ) that is compatible with the algebraic structure of X in the sense that it satisfies the following two axioms: 1) If x≥y, then x+z≥y+z holds for all z in X. 2) If x≥y, then λx≥λy holds for all λ≥0. A vector lattice is an ordered vector space X with the additional property that for each pair of vectors x and y in X the least upper bound and the greatest lower bound of the set {x , y } both exist in X. A norm on a vector lattice is said to be a lattice norm whenever In case of conditions. A vector lattice equipped with a lattice norm is known as a normed vector lattice. If a normed vector lattice is also norm complete, then it is referred to as a Banach lattice. A Banach lattice X is said to be: 1) An AL-space (abstract L-space), whenever its norm is a L-norm. 2) An AM-space (abstract M-space), whenever its norm is a M-norm. One of the aims in this thesis is to study the existence of fixed points of non expansive mappings in AM-spaces. First we prove a general fixed point theorem for non expansive mappings in dual spaces and then we draw some consequences for non expansive mappings acting in AM-spaces which are dual to AL-spaces. The next aim is to study the existence of fixed points of the subset of all convergent sequences. We show that there exists a non-weakly compact, closed, bounded, convex subset W of the Banach space of convergent sequences in a real field such that every non expansive mapping T: W→W has a fixed point.

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