Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras - Hark-Mahn Kim; Hwan-Yong Shin (Mathematics, 2020)
In this paper, we find the solution of the following quadratic functional equation <semantics>n∑1≤i<j≤nQ<mfenced separators="" open="(" close=")">xi−xj</mfenced>=<msubsup>∑i=1n</msubsup>Q<mfenced separators="" open="(" close=")">∑j≠ixj−(n−1)xi</mfenced></semantics>, which is derived from the gravity of the n distinct vectors <semantics>x1,⋯,xn</semantics> in an inner product space, and prove that the stability results of the <semantics>A</semantics>-quadratic mappings in <semantics>μ</semantics>-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and <semantics>β</semantics>-homogeneous property.