We give the definition of quasinearly subharmonic functions,
point out that this function class includes, among others, subharmonic
functions, quasisubharmonic functions, nearly subharmonic functions
(in a slightly generalized sense) and almost subharmonic functions (essentially). Moreover, we give basic properties of quasinearly subharmonic functions, and, among others, we characterize quasinearly subharmonicity with the aid of quasihyperbolic metric.
Keywords: Subharmonic, nearly subharmonic, quasinearly subharmonic, properties of quasinearly subharmonic functions, quasihyperbolic metric
