In this paper, We define Jordan algebra bundles of finite type and we give one-one correspondence between Jordan algebra bundles of finite type and Jordan rings.

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation Snk=2 Ski1=2 Sk+1i2=i1+1 · Sn in-k+1=in-k+1 ¦ (Sni=1, i ¹i1, ···, in-k+1 ci -Sn-k+1r=1 cir) + ¦ (Sni=1 ci) -2n-1 ¦ (c1)=0, where n is an integer greater than 1.

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Let A be a unital R-algebra and M be a unital A- bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.