Du, Wei-ShihKarapınar, ErdalKarapinar, ErdalMathematics2024-07-052024-07-052013131687-181210.1186/1687-1812-2013-3442-s2.0-84896460341https://doi.org/10.1186/1687-1812-2013-344https://hdl.handle.net/20.500.14411/106KARAPINAR, ERDAL/0000-0002-6798-3254In 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.eninfo:eu-repo/semantics/openAccessbest proximity pointCaristi-type cyclic mapMT-function (R-function)MT-cyclic contractionCaristi-type fixed point theoremArticleWOS:000209289900001