Stability of additive-quadratic ρ-functional equations in Banach spaces: a fixed point approach

---

Park C., Kim S. O., ALACA C.

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, sa.3, ss.1252-1262, 2017 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Basım Tarihi: 2017
• Doi Numarası: 10.22436/jnsa.010.03.34
• Dergi Adı: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
• Sayfa Sayıları: ss.1252-1262
• Anahtar Kelimeler: Hyers-Ulam stability, additive-quadratic rho-functional equation, fixed point method, Banach space
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Let M(1)f (x, y) : = 3/4 f (x + y) -1/4 f (-x -y) + 1/4 f (x - y) + 1/4 f(y - x) -f (x) -f (y), M(2)f(x, y) : = 2f( x + y/2) + f ( x - y/2 ) + f ( y - x/2 ) -f (x) -f (y). We solve the additive-quadratic rho-functional equations M(1)f (x, y) = rho M(2)f(x, y), (1) and M(2)f(x, y) = rho M(1)f (x, y), (2) where rho is a fixed nonzero number with rho not equal 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive-quadratic rho-functional equations (1) and (2) in Banach spaces. (C)2017 All rights reserved.