Let A, B be two unital C^＊-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h ： A →B which satisfies h（2^nuy） = h（2^nu）h（y） for all u ∈ U（A）, all y ∈ A, and a...Let A, B be two unital C^＊-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h ： A →B which satisfies h（2^nuy） = h（2^nu）h（y） for all u ∈ U（A）, all y ∈ A, and all n = 0,1,2,..., is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of ,-homomorphisms on unital C^＊-algebras.展开更多
Let Pn be the class of polynomials of degree at most n. Rather and Shah [15] proved that if P∈Pn and P（z） 6=0 in｜z｜〈1, then for every R〉0 and 0≤q〈∞,｜B[P（Rz）]｜q≤｜RnB[zn]＋λ0｜q｜1＋zn｜q ｜P（z）｜q, w...Let Pn be the class of polynomials of degree at most n. Rather and Shah [15] proved that if P∈Pn and P（z） 6=0 in｜z｜〈1, then for every R〉0 and 0≤q〈∞,｜B[P（Rz）]｜q≤｜RnB[zn]＋λ0｜q｜1＋zn｜q ｜P（z）｜q, where B is a Bn-operator. In this paper, we prove some generalization of this result which in particular yield-s some known polynomial inequalities as special. We also consider an operator Dαwhich maps a polynomial P（z） into DαP（z）：=nP（z）＋（α-z）P′（z） and obtain exten-sions and generalizations of a number of well-known Lq inequalities.展开更多
文摘Let A, B be two unital C^＊-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h ： A →B which satisfies h（2^nuy） = h（2^nu）h（y） for all u ∈ U（A）, all y ∈ A, and all n = 0,1,2,..., is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of ,-homomorphisms on unital C^＊-algebras.
文摘Let Pn be the class of polynomials of degree at most n. Rather and Shah [15] proved that if P∈Pn and P（z） 6=0 in｜z｜〈1, then for every R〉0 and 0≤q〈∞,｜B[P（Rz）]｜q≤｜RnB[zn]＋λ0｜q｜1＋zn｜q ｜P（z）｜q, where B is a Bn-operator. In this paper, we prove some generalization of this result which in particular yield-s some known polynomial inequalities as special. We also consider an operator Dαwhich maps a polynomial P（z） into DαP（z）：=nP（z）＋（α-z）P′（z） and obtain exten-sions and generalizations of a number of well-known Lq inequalities.
