Solution for 3rd order Cauchy Difference Equation in Free Monoid - Pradeep, M (International Journal of Membrane Science and Technology, 2023)
— Let k: C ? D be a function, where (C,.) is a Group and (D,+) is an Abelian Group. In this article, the Third Order Cauchy difference of k:E(3) k (c1,c2,c3,c4)= k(c1c2c3c4) – k(c1c2c3) – k(c1c3c4) – k (c1c2c3c4) –k (c2c3c4) + k(c1c2) + k (c1c3) +k(c1c4)+k(c2c3)+ k(c2c4)+k(c3c4) –k(c1) – k(c2) –k(c3) –k(c4) ? c1,c2,c3,c4 C is studied. We give solutions of E(3)k=0 on Free Monoid.