Abstract
This work aims to study of the stability of two generalizations of the functional equa- tion f(pr,qs)+f(ps,qr )= f(p,q) f(r,s), namely (i) f(pr,qs)+g(ps,qr )= h(p,q)h(r,s) ,a nd (ii) f(pr,qs)+g(ps,qr )= h(p,q)k(r,s) for all p,q,r,s ∈ G ,w hereG is a commutative semi- group. Thus this work is a continuation of our earlier works (15 )a nd (16), and the functional equations studied here arise in the characterizations of symmetrically compositive sum form distance measures.
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