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

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.

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

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)

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

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