A counterexample on a theorem by Khojasteh, Goodarzi, and Razani
Apstrakt
In the paper by Khojasteh et al. (2010), the authors tried to generalize Branciari's theorem, introducing the new integral type contraction mappings. In this note we give a counterexample on their main statement (Theorem 2.9). Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, where the cone is taken from the infinite dimensional space.
Izvor:
Fixed Point Theory and Applications, 2010, 2010Izdavač:
- SpringerOpen
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Aranđelović, Ivan AU - Keckić, Dragoljub J. PY - 2010 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1006 AB - In the paper by Khojasteh et al. (2010), the authors tried to generalize Branciari's theorem, introducing the new integral type contraction mappings. In this note we give a counterexample on their main statement (Theorem 2.9). Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, where the cone is taken from the infinite dimensional space. PB - SpringerOpen T2 - Fixed Point Theory and Applications T1 - A counterexample on a theorem by Khojasteh, Goodarzi, and Razani VL - 2010 DO - 10.1155/2010/470141 ER -
@article{ author = "Aranđelović, Ivan and Keckić, Dragoljub J.", year = "2010", abstract = "In the paper by Khojasteh et al. (2010), the authors tried to generalize Branciari's theorem, introducing the new integral type contraction mappings. In this note we give a counterexample on their main statement (Theorem 2.9). Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, where the cone is taken from the infinite dimensional space.", publisher = "SpringerOpen", journal = "Fixed Point Theory and Applications", title = "A counterexample on a theorem by Khojasteh, Goodarzi, and Razani", volume = "2010", doi = "10.1155/2010/470141" }
Aranđelović, I.,& Keckić, D. J.. (2010). A counterexample on a theorem by Khojasteh, Goodarzi, and Razani. in Fixed Point Theory and Applications SpringerOpen., 2010. https://doi.org/10.1155/2010/470141
Aranđelović I, Keckić DJ. A counterexample on a theorem by Khojasteh, Goodarzi, and Razani. in Fixed Point Theory and Applications. 2010;2010. doi:10.1155/2010/470141 .
Aranđelović, Ivan, Keckić, Dragoljub J., "A counterexample on a theorem by Khojasteh, Goodarzi, and Razani" in Fixed Point Theory and Applications, 2010 (2010), https://doi.org/10.1155/2010/470141 . .