By a counter example we show that two continuous functions defined on a compact metric space satisfying a certain semi metric need not have a common periodic point.
BAKER, C. W. (1994). θ-R-CONTINUOUS FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 1994(), 73-78. https://doi.org/10.1155/S0161171294000116
SAVVOPOULOU, C. K., & JANKOVIC, D. (1992). R-CONTINUOUS FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 1992(), 57-64. https://doi.org/10.1155/S0161171292000073
KILIÇMAN, A., & SALLEH, Z. (2006). SOME RESULTS ON (δ-PRE, s)-CONTINUOUS FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 2006(), 959-969-076. https://doi.org/10.1155/IJMMS/2006/39320