On a problem by K. Nikodem

Abstract

Abstract. Concerning a problem raised by K. Nikodem, we prove the following statement.

Additive ρ --functional inequalities

“…Gilányi [9] and Fechner [5] proved the Hyers-Ulam stability of the functional inequality (3). Park, Cho and Han [12] proved the Hyers-Ulam stability of additive functional inequalities.…”

Additive ρ -functional inequalities in normed spaces

“…Gilányi [11] and Fechner [7] proved the Hyers-Ulam stability of the functional inequality (1.1). Park, Cho and Han [16] proved the Hyers-Ulam stability of additive functional inequalities.…”

Quadratic $\rho$-functional inequalities and equations

“…Gilányi [8] and Fechner [5] proved the Hyers-Ulam stability of the functional inequality (1.3). Park, Cho and Han [11] proved the Hyers-Ulam stability of additive functional inequalities.…”