On stability of the functional equation of p-Wright affine functions in (2,α)-Banach spaces
El-hady, E. (2019). On stability of the functional equation of p-Wright affine functions in (2,α)-Banach spaces. EKB Journal Management System, 27(1), 1-9. doi: 10.1186/s42787-019-0024-y
El-sayed El-hady. "On stability of the functional equation of p-Wright affine functions in (2,α)-Banach spaces". EKB Journal Management System, 27, 1, 2019, 1-9. doi: 10.1186/s42787-019-0024-y
El-hady, E. (2019). 'On stability of the functional equation of p-Wright affine functions in (2,α)-Banach spaces', EKB Journal Management System, 27(1), pp. 1-9. doi: 10.1186/s42787-019-0024-y
El-hady, E. On stability of the functional equation of p-Wright affine functions in (2,α)-Banach spaces. EKB Journal Management System, 2019; 27(1): 1-9. doi: 10.1186/s42787-019-0024-y

On stability of the functional equation of p-Wright affine functions in (2,α)-Banach spaces

Journal of the Egyptian Mathematical Society
Volume 27, Issue 1, 2019, Pages 1-9    PDF (426.54 K)
DOI: 10.1186/s42787-019-0024-y
Author
El-sayed El-hady1, 2
1Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia
2Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egyp
Abstract
Stability of functional equations has recent applications in many fields. We show that
the stability results obtained by J. Brzd ˛ek and concerning the functional equation of the
p-Wright affine function:
f(px1 + (1 − p)x2) + f((1 − p)x1 + px2) = f(x1) + f(x2),
can be proved also in (2,α)-Banach spaces, for some real number α ∈ (0, 1). This is
done using some fixed-point theorem.
Keywords
Hyers-Ulam stability; p-Wright convexity; Affine function; Banach spaces
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