| Summary: | 碩士 === 國立中央大學 === 數學研究所 === 96 === This thesis is concerned with two subjects of research; Hardy-Hilbert type inequalities and the stability of Cauchy additive mappings. The following are done : 1) to extend B. Yang''s result on the norm of a bounded self- adjoint integral operator T : L2 (0,∞) → L2 (0,∞) and its applications to Hardy-Hilbert type integral inequalities from the space L2 (0,∞) to the space Lp (0,∞) with p > 1 ; 2) to generalize Rassias''s theorem on the stability of Cauchy additive mappings ; 3) to give a correct proof of Park et al''s theorem in [6]; 4) to approximate the odd part of a certain vector mapping by a unique group homomorphism and ring homomorphism, respectively.
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