Stability of some functional equations related to distance measures—I

The present work aims to study the stability of the following three functional equations: (i) f(pr,qs)+f(ps,qr)=f(p,q)f(r,s), (ii) f(pr,qs)+f(ps,qr)=f(p,q)g(r,s), and (iii) f(pr,qs)+f(ps,qr)=g(p,q)f(r,s) for all p,q,r,s∈(0,1)p,q,r,s∈(0,1). The first functional equation arises in the characterization of symmetrically compositive sum form distance measures.