Ternary Derivation-Homomorphism Functional Inequalities

Jung Rye Lee (), Choonkil Park () and Michael Th. Rassias
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Jung Rye Lee: Daejin University
Choonkil Park: Hanyang University
Michael Th. Rassias: Hellenic Military Academy

A chapter in Geometry and Non-Convex Optimization, 2025, pp 263-277 from Springer

Abstract: Abstract In this chapter, we introduce and solve the following additive-additive ( s , t ) $$(s,t)$$ -functional inequality: ∥ 3 g x + y + z 3 − g ( x ) − g ( y ) − g ( z ) ∥ $$\displaystyle \|3 g\left (\frac {x+y+z}{3}\right )-g(x)-g(y)-g(z)\| $$ + ∥ 3 h x + y + z 3 + h ( x −2 y + z ) + h ( x + y −2 z ) −3 h ( x ) ∥ $$\displaystyle +\|3h\left (\frac {x+y+z}{3}\right )+ h(x-2y+z) + h(x+y-2z)-3 h(x) \| $$ ≤ s g x + y + z − g ( x ) − g ( y ) − g ( z ) $$\displaystyle \le \left \|s\left ( g\left (x+y+z\right ) -g(x) -g(y)-g(z)\right )\right \| $$ + t h ( x + y + z ) + h ( x −2 y + z ) + h ( x + y −2 z ) −3 h ( x ) , $$\displaystyle + \left \|t \left ( h(x+y+z) + h(x-2y+z) + h(x+y-2z)-3 h(x) \right ) \right \| , $$ where s and t are fixed nonzero complex numbers with | s |

Date: 2025
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DOI: 10.1007/978-3-031-87057-6_10

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