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Fixed point of continuous mappings defined on an arbitrary intervalAlagoz, OsmanGunduz, BirolAkbulut, SezginContinuous mappingConvergence theoremFixed pointIn this work, we consider an iterative method given by Karaca and Yildirim [6] to approximate fixed point of continuous mappings defined on an arbitrary interval. Then, we give a necessary and sufficient condition for convergence theorem. We also compare the rate of convergence between the other iteration methods. Finally, we provide a numerical example which supports our theoretical results. Our findings improve corresponding results in the contemporary literature. © 2019 Miskolc University Press.University of Miskolc2019Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/14132https://doi.org/10.18514/mmn.2019.25091787-2405enMiskolc Mathematical Notesinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/14132