Stability of the seventh-order functional Equations in the β-Gaussian space

Document Type: research paper

Authors

1 ph. D. Student, Department of Pure Mathematics (Mathematical Analysis), Faculty of Basic Science, Islamic Azad University, Science and Research Branch, Tehran, Iran.

2 Associate Professor, Department of Mathematics‎, Faculty of Science, Central Tehran Branch‎, Islamic Azad University‎, Tehran‎, ‎Iran.

3 Assistant Professor, Department of Pure Mathematics (Mathematical Analysis), Faculty of Basic Science, Islamic Azad University, Science and Research Branch, Tehran, Iran

Abstract

The purpose of this paper is to solve the seventh-order functional equation as follows:
 ---------------------------
Next, we study the stability of this type of functional equation. Clearly, the function ----------  holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.
 

Keywords


Article Title [Persian]

پایداری معادلات تابعی مرتبه هفتین درفضای β-گاوسی

Authors [Persian]

  • ناصر غفوری عدل 1
  • داود ابراهیمی بقاء 2
  • محمدصادق عسگری 2
  • مهدی آژینی 3
1 گروه ریاضی محض (آنالیز ریاضی)، دانشگاه آزاد اسلامی واحد علوم و تحقیقات، تهران، ایران
2 گروه ریاضی و آمار، دانشکده علوم پایه، دانشگاه آزاد اسلامی واحد تهران مرکزی، تهران، ایران
3 گروه ریاضی محض (آنالیز ریاضی)، دانشگاه آزاد اسلامی واحد علوم و تحقیقات، تهران، ایران
Abstract [Persian]

هدف این مقاله، حل معادله تابعی از مرتبه هفتم به شکل:
 -----------------------------------
 
و بررسی پایداری این نوع معادله تابعی می­باشد. واضح است که تابع  ------- در معادله تابعی فوق صدق می­کند و ما پایداری هایرز-اولام را برای این نوع معادله تابعی در فضاهای باناخ -گاوسی ثابت می­کنیم.

Keywords [Persian]

  • معادلات تابعی
  • پایداری نرم β-گاوسی
  • (β؛ p)-قضایای باناخ
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