Properties of Subadditive Functions and Its Analogs
TANG Jianguo(Department of Mathematics and Computational Science,Hunan University of Science and Engineering,Yongzhou 425006,China)
It is proved that when all the ratios of the generic term of a subaddtive sequence to its ordinal number form a lower bounded sequence,the ratio sequence must have limitation.From this,it is proved that when all the ratios of a subaddtive function defined on the interval(0,+∞) to the value of its variable form a bounded function,the subaddtive function must have supremum and infimum functions,which are homogeneously linear functions.Furthermore,its analogs are also investigated and some important results are derived in the paper.


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