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中文摘要：
本文研究了R^1的非连通紧子集上的两个连续函数和的图像的盒维数估计的问题.利用构造反例的方法得到了与已有的结果完全不同的结论.通过引入适当的参量,进一步研究了R^n的非空有界子集上的两个函数和的图像的上、下盒维数估计,得到了其上、下界,并且构造了例子说明所得的上、下界能够达到.
英文摘要：
This article concerns the estimate for the box dimension of the graph of the sum of two continuous functions over the same disconnected compact subset of R^1,and derives a result completely different from the known result.By constructing a counterexample,we discuss the estimates for the upper and lower box dimensions of the graph of the sum of two functions over the same nonempty bounded subset of R^n,and the upper and lower bounds are obtained via some appropriate parameters.Furthermore,an example is constructed to confirm that the upper and lower bounds can be attained.
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