Abstract
We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (<TEX>${\alpha},{\beta}$</TEX>)-metric be a weakly-Berwald space and the Finsler spaces with some special (<TEX>${\alpha},{\beta}$</TEX>)-metrics be weakly-Berwald spaces, respectively.
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