In this paper,we introduce and solve the following additive(ρ1,ρ2)-functional inequalities‖f(x+y+z)-f(x)-f(y)-f(z)‖≤‖ρ1(f(x+z)-f(x)-f(z))‖+‖ρ2(f(y+z)-f(y)-f(z))‖,whereρ1 andρ2 are fixed nonzero complex nu...In this paper,we introduce and solve the following additive(ρ1,ρ2)-functional inequalities‖f(x+y+z)-f(x)-f(y)-f(z)‖≤‖ρ1(f(x+z)-f(x)-f(z))‖+‖ρ2(f(y+z)-f(y)-f(z))‖,whereρ1 andρ2 are fixed nonzero complex numbers with|ρ1|+|ρ2|<2.Using the fixed point method and the direct method,we prove the Hyers–Ulam stability of the above additive(ρ1,ρ2)-functional inequality in complex Banach spaces.Furthermore,we prove the Hyers–Ulam stability of hom-derivations in C^*-ternary algebras.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11761074)supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(Grant No.NRF-2017R1D1A1B04032937)The author is grateful to anonyme reviewers for their valuable com ments and suggestions.
文摘In this paper,we introduce and solve the following additive(ρ1,ρ2)-functional inequalities‖f(x+y+z)-f(x)-f(y)-f(z)‖≤‖ρ1(f(x+z)-f(x)-f(z))‖+‖ρ2(f(y+z)-f(y)-f(z))‖,whereρ1 andρ2 are fixed nonzero complex numbers with|ρ1|+|ρ2|<2.Using the fixed point method and the direct method,we prove the Hyers–Ulam stability of the above additive(ρ1,ρ2)-functional inequality in complex Banach spaces.Furthermore,we prove the Hyers–Ulam stability of hom-derivations in C^*-ternary algebras.
