OICC Press Mathematical Sciences 2251-7456 15 3 (September 2021) 2021 02 22 Strong and pure fixed point properties of mappings on normed spaces 10.1007/s40096-021-00380-x EN Hüseyin Işık Department of Engineering Science, Bandırma Onyedi Eylül University, Bandırma, Balıkesir, 10200, TR Vahid Parvaneh Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, IR Mohammad Reza Haddadi Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, IR Journal Article 2021 02 22 Abstract In this paper, the concept of strong fixed point property of a mapping is defined. The relationship between an approximating fixed point sequence and compactness is studied. The notion of a center set for a mapping is introduced. Some necessary and sufficient conditions for existence of mappings admitting a center set are presented. The results proved herein extend, generalize and improve some well-known comparable results.