Remarks on fixed point assertions in digital topology, 3

• Boxer, Laurence ^[1]
  1. [1] Niagara University

     Niagara University

     Town of Lewiston, Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 2, 2019, págs. 349-361
• Idioma: inglés
• DOI: 10.4995/agt.2019.11117
• Enlaces
  • Texto completo
• Resumen

  • We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality under "usual" conditions; or that we improve upon.

• Referencias bibliográficas
  • L. Boxer, A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456
  • L. Boxer, Generalized normal product adjacency in digital topology, Applied General Topology 18, no. 2 (2017), 401-427. https://doi.org/10.4995/agt.2017.7798
  • L. Boxer, Remarks on fixed point assertions in digital topology, 2, Applied General Topology 20, no. 1 (2019), 155-175. https://doi.org/10.4995/agt.2019.10667
  • L. Boxer, O. Ege, I. Karaca, J. Lopez and J. Louwsma, Digital fixed points, approximate fixed points and universal functions, Applied General...
  • L. Boxer and P. C. Staecker, Remarks on fixed point assertions in digital topology, Applied General Topology 20, no. 1 (2019), 135-153. https://doi.org/10.4995/agt.2019.10474
  • G. Chartrand and L. Lesniak, Graphs & Digraphs, 2nd ed., Wadsworth, Inc., Belmont, CA, 1986.
  • S. Dalal, Common fixed point results for weakly compatible map in digital metric spaces, Scholars Journal of Physics, Mathematics and Statistics...
  • O. Ege and I. Karaca, Digital homotopy fixed point theory, Comptes Rendus Mathematique 353, no. 11 (2015), 1029-1033. https://doi.org/10.1016/j.crma.2015.07.006
  • J. Haarmann, M. P. Murphy, C. S. Peters and P. C. Staecker, Homotopy equivalence of finite digital images, Journal of Mathematical Imaging...
  • S.-E. Han, Banach fixed point theorem from the viewpoint of digital topology, Journal of Nonlinear Science and Applications 9 (2016), 895-905....
  • D. Jain and A.C. Upadhyaya, Weakly commuting mappings in digital metric spaces, International Advanced Research Journal in Science, Engineering...
  • K. Jyoti and A. Rani, Digital expansions endowed with fixed point theory, Turkish Journal of Analysis and Number Theory 5, no. 5 (2017), 146-152....
  • A. Rosenfeld, 'Continuous' functions on digital pictures, Pattern Recognition Letters 4 (1986), 177-184. https://doi.org/10.1016/0167-8655(86)90017-6
  • B. Samet, C. Vetro,and P. Vetro, Fixed point theorem for $alpha-psi$-contractive type mappings, Nonlinear Analysis 75 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014
  • S. Sessa, On a weak commutative condition of mappings in fixed point considerations, Publications De l'Institut Mathematique, Nouvelle...