On the characterization of generalized (m, n)-Jordan *-derivations in prime rings

Let 𝒜{\mathcal{A}}be a prime ring equipped with an involution ‘*{*}’ of order 2 and let m≠n{m\neq n}be some fixed positive integers such that 𝒜{\mathcal{A}}is 2⁢m⁢n⁢(m+n)⁢|m-n|{2mn(m+n)|m-n|}-torsion free. Let 𝒬m⁢s⁢(𝒜){\mathcal{Q}_{ms}(\mathcal{A})}be the maximal symmetric ring of quotients of 𝒜{\mathcal{A}}and consider the mappings ℱ{\mathcal{F}}and 𝒢:𝒜→𝒬m⁢s⁢(𝒜){\mathcal{G}:\mathcal{A}\to\mathcal{Q}_{ms}(\mathcal{A})}satisfying the relations