scholarly journals Stability of a general p-radical functional equation related to additive mappings in 2-Banach spaces

2021 ◽  
Vol 40 (1) ◽  
pp. 49-71
Author(s):  
Sadeq A. A. AL-Ali ◽  
Muaadh Almahalebi ◽  
Youssfi Elkettani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Radical Functional Equation ◽  
Additive Mappings

In this paper, we introduce and solve a new general p-radical functional equation Also, we investigate some stability and hyperstability results for the considered equation in 2-Banach spaces. In addition, we prove the hyperstability of the inhomogeneous p-radical functional equation

scholarly journals Some hyperstability results of a p-radical functional equation related to Drygas mappings in non-Archimedean Banach spaces

2021 ◽  
Vol 40 (1) ◽  
pp. 153-174
Author(s):  
Mustapha Esseghyr Hryrou ◽  
Ahmed Nuino ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Natural Number ◽  
Banach Spaces ◽  
Point Theorem ◽  
Radical Functional Equation

The aim of this paper is to introduce and solve the following pradical functional equation related to Drygas mappings f(√(p&x^p+ y^p ))+f(√(p&x^p+ y^p ))=2f(x)+f(y)+f(-y),x,y ∈R, where f is a mapping from R into a vector space X and p ≥ 3 is an odd natural number. Using an analogue version of Brzdȩk’s fixed point theorem [14], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous p-radical functional equation related to Drygas mappings f(√(p&x^p+ y^p ))+f(√(p&x^p+ y^p ))=2f(x)+f(y)+f(-y)+G(x,y)

scholarly journals Some hyperstability results of a p-radical functional equation related to quartic mappings in non-archimedean Banach spaces

2021 ◽  
Author(s):  
Ahmed Nuino ◽  
Mustapha Esseghyr Hryrou ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Natural Number ◽  
Banach Spaces ◽  
Point Theorem ◽  
Radical Functional Equation ◽  
Quartic Mapping

The aim of this paper is to introduce and solve the following p-radical functional equation related to quartic mappings. where f is a mapping from R into a vector space X and p ≥ 3 is an odd natural number. Using an analogue version of Brzd¸ek’s fixed point theorem [13], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous p-radical functional equation related to quartic mapping.

scholarly journals HUR-approximation of an ELTA functional equation

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

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