TY - JOUR AU - Du, Wei-Shih AU - Karapinar, Erdal PY - 2013 DA - 2013/12/16 TI - A note on Caristi-type cyclic maps: related results and applications JO - Fixed Point Theory and Applications SP - 344 VL - 2013 IS - 1 AB - In this note, we first introduce the concept of Caristi-type cyclic map and present a new convergence theorem and a best proximity point theorem for Caristi-type cyclic maps. It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property. Some best proximity point results and convergence theorems in the literature have been derived from our main results. Consequently, the presented results improve, extend and generalize some of the existence results on the topic. SN - 1687-1812 UR - https://doi.org/10.1186/1687-1812-2013-344 DO - 10.1186/1687-1812-2013-344 ID - Du2013 ER -