The subject of this paper is a systematic study of inequalities of the form (1 . μ )M 1 + μ M 3 M 2 (1 . ν )M 1 + ν M 3 which cover Neuman-S ′ andor mean and some classical means. Furthermore, following inequali- ties with optimal parameters were proved: μ 1 H(s,t) +(1 . μ ) 1 NS (s,t) 1 A(s,t) ν 1 H(s,t) +(1 . ν ) 1 NS(s,t) and μ 1 H(s,t) +(1 . μ ) 1 N(s,t) 1 NS (s,t) ν 1 H (s,t) +(1 . ν ) 1 N(s,t)
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