摘要
We prove that if f and g are functions from the reals into the reals such that the composition of g with f is continuous and f is both Darboux and surjective, then g is continuous. We also prove that continuous and Darboux can be interchanged in the above statement.
延伸閱讀
- Dziok, J. (2015). Classes of Harmonic Functions Defined by Subordination. Abstract and Applied Analysis, (2015), 113-121. https://doi.org/10.1155/2015/756928
- XIAO, J. (1997). SOME PROPERTIES AND CHARACTERIZATIONS OF A-NORMAL FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 1997(), 503-510. https://doi.org/10.1155/S0161171297000689
- BAKER, C. W. (1994). θ-R-CONTINUOUS FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 1994(), 73-78. https://doi.org/10.1155/S0161171294000116
- Ezeafulukwe, U. A., & Darus, M. (2014). Some Properties of Certain Class of Analytic Functions. International Journal of Mathematics and Mathematical Sciences, 2014(), 206-210. https://doi.org/10.1155/2014/358467
- Owa, S., Hayami, T., & Kuroki, K. (2007). Some Properties of Certain Analytic Functions. International Journal of Mathematics and Mathematical Sciences, 2007(), 1277-1285. https://doi.org/10.1155/2007/91592