دراسة استقرار معادلة كوشي الدالية

الموضوعات

علوم بحتة وطبيعية

روابط وملفات

التعريف والنوع

رقم الوثيقة

02a872e6-d867-4edf-9de4-198adb097553

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

1966501_1.pdf

بيانات النشر

ترجمة العنوان

Study of the Stability of Cauchy's Functional Equation

ألقاب المؤلفين

[{"name_ar":"حمزة أكرم الآغا","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"محمد الشيخ","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

Arabic

المصدر والدورية

اسم المصدر

دراسة استقرار معادلة كوشي الدالية

المحتوى والصفحات

عدد الصفحات

139

ترجمة الملخص

The Stability of Functional Equations in general and Cauchy Functional Equation in particular have many applications in different fields like Math, Physics, Economy ...etc.Stability Theory appeared when Prof. Ulam asked his famous question in 1940 :Let and be a group and a metric group with a metric , respectively .Given , does there exist a such that if a function satisfies the inequality for all ,then there exists a homomorphism with for all ?D.H. Hyers answered this question in 1941.This answer was the starting point for the Ulam Stability Theory.Then Stability Theorems have followed such as(Hyers–Ulam–Rassi as and Gavrruta Stability) and Generalizations ( The most important Rassi as–semral, Isa–Rassias and Jung Generalization ) .Opposite examples (The most important is Gajda example and two examples for Rassi as and semral ) show that the mentioned theorems are incorrect if.In addition to the previous generalizations that all revolve around the study of the majorant existed in the right end of the inequality in the theorems, scientists tried to generalize the functions space domain in the stability theorems. Ratz and Forti studied the Stability Cauchy Equation on the commutative semi group and amenable semi group . In 1985, For ti gave example showed that Cauchy Functional Equation is not stable for a free group generated by two elements . Gajda and Szekelyhidi generalized Codo main functions mentioned in Stability theorems and they used topological vector space for that purpose.In this thesis we demonstrated most of the researches related with the stability Cauchy Functional Equation since 1940 until 2013 and explained most of the proofs that mentioned in the references .

إشراف وإعداد

الإشراف

محمد الشيخ

الإعداد

حمزة أكرم الآغا

الاقتباسات الببليوغرافية