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Let(   u   m  n  s    )    ${(u_{mns})}$    be a ( C ,1,1,1) summable triple sequence of real numbers. We give one-sided Tauberian conditions of Landau and Hardy type under which(   u   m  n  s    )    ${(u_{mns})}$    converges in Pringsheim's sense. We prove that(   u   m  n  s    )    ${(u_{mns})}$    converges in Pringsheim's sense if(   u   m  n  s    )    ${(u_{mns})}$    is slowly oscillating in certain senses. Moreover, we extend a Tauberian theorem given by Móricz [Studia Math. 110 (1994), 83–96] for double sequences to triple sequences.

Some classical Tauberian theorems for ( C ,1,1,1) summable triple sequences