Stability and nonstability of octadecic functional equation in multi-normed spaces

Abstract

In this paper, we introduce octadecic functional equation. Moreover, we prove the stability of the octadecic functional equation in multi-normed spaces by using the fixed point method.Mathematics Subject Classification 39A11 · 39B52

Stability of Pinelas-Septoicosic functional equation

“…→ 0 as i → ∞ for all x ∈ X. Thus, it follows that the sequence f (2 a x) 2 a (27) is Cauchy in Y and so it converges. Therefore, the mapping G : X → Y is defined by 27) is well defined for all x ∈ X.…”

“…for all x ∈ X. It follows from (57), we get 27 (58) for all x ∈ X. Now, replacing x by 2x and dividing 2 27 in (58), we get…”

“…for all x ∈ X. From ( 58) and ( 59), we obtain 27 (60) for all x ∈ X. Generalizing for any positive integer a, we get…”

“…Therefore, the mapping G : X → Y is defined by 27) is well defined for all x ∈ X. In order to show that G satisfies (11) by interchanging (x, y) by (2 a x, 2 a y) in (46) and then dividing by 2 a (27) , we get…”

“…Murali Ramdoss et al,in [24] carry out the Hyers-Ulam stability of duodecic functional equation in Multi-Banach spaces using fixed point method and also introduced the tredecic functional equation in [25] and investigated and established the generalized Ulam-Hyers stability of this functional equation in matrix normed spaces by using the fixed point method, septndecic functional equation [26] in matrix normed spaces. Nazarlanpoor et al, introduced the Octadecic functional equation in [27] and they proved the stability for multi normed space by using standard fixed point method and also nonadecic functional equation [28] in Multi-Banach spaces. Murali et al, establish the general solution for the viginti duo functional equation in [29] and determined the Hyers-Ulam stability for a the viginti duo functional equation in Multi-Banach spaces by using fixed point technique.…”