Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Turkish Journal of Analysis and Number Theory. 2017, 5(5), 146-152
DOI: 10.12691/tjant-5-5-1
Open AccessArticle

Digital Expansions Endowed with Fixed Point Theory

Kumari Jyoti1 and Asha Rani1,

1Department of Mathematics, SRM University, Haryana, Sonepat- 131001, India

Pub. Date: July 11, 2017

Cite this paper:
Kumari Jyoti and Asha Rani. Digital Expansions Endowed with Fixed Point Theory. Turkish Journal of Analysis and Number Theory. 2017; 5(5):146-152. doi: 10.12691/tjant-5-5-1


The area of fixed point theory is very active in many branches of mathematics and other related disciplines such as image processing, computer vision, applied mathematics, etc. The main goal in this theory is to solve many problems and to give some useful applications. The aim of this paper is to associate fixed point theory and digital images.

expansive mappings digital-α-ψ– expansive mappings fixed point theorems digital metric space

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/


[1]  L. E. S. Brouwer, Uber Abbildungen Von Mannigfaltigkeiten, Math. Ann., 77(1912), 97-115.
[2]  L. Boxer, Digitally Continuous Functions, Pattern Recognition Letters, 15 (1994), 833-839.
[3]  L. Boxer, Properties of Digital Homotopy, J. Math. Imaging Vis., 22(2005), 19-26.
[4]  L. Boxer, A Classical Constructions for The Digital Fundamental Group, J. Math. Imaging Vis., 10(1999), 51-62.
[5]  L. Boxer, Digital Products, Wedges and Covering Spaces, J. Math. Imaging Vis., 25(2006), 159-171.
[6]  L. Boxer, Continuous Maps on Digital Simple Closed Curves, Appl. Math., 1(2010), 377-386.
[7]  L. Boxer, O. Ege, I. Karaca, J. Lopez and J. Louwsma, Digital fixed points, approximate fixed points, and universal functions, Applied General Topology, 17(2), 159-172 (2016).
[8]  O. Ege, I. Karaca, Fundamental Properties of Simplicial Homology Groups for Digital Images, American Journal of Computer Technology and Application, 1(2013), 25-42.
[9]  O. Ege, I. Karaca, Lefschetz Fixed Point Theorem for Digital Images, Fixed Point Theory Appl., 2013(2013), 13 pages.
[10]  O. Ege, I. Karaca, Applications of The Lefschetz Number to Digital Images, Bull. Belg. Math. Soc. Simon Stevin, 21(2014), 823-839.
[11]  O. Ege, I.karaca, Banach Fixed Point Theorem for Digital Images, J. Nonlinear Sci. Appl., 8(2015), 237-245.
[12]  O. Ege and I. Karaca, Digital homotopy fixed point theory, Comptes Rendus Mathematique, 353(11), 1029-1033 (2015).
[13]  O. Ege, Complex valued Gb -metric spaces, Journal of Computational Analysis and Applications, 21(2), 363-368 (2016).
[14]  O. Ege and I. Karaca, Digital fibrations, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 87(1), 109-114 (2017).
[15]  O. Ege and I. Karaca, Nielsen fixed point theory for digital images, Journal of 2 Computational Analysis and Applications, 22(5), 874-880 (2017).
[16]  G. T. Herman, Oriented Surfaces in Digital Spaces, CVGIP: Graphical Models and Image Processing, 55(1993), 381-396.
[17]  I. Karaca, O. Ege, Some Results on Simplicial Homology Groups of 2D Digital Images, Int. J. Inform. Computer Sci., 1(2012), 198-203.
[18]  T. Y. Kong, A Digital Fundamental Group, Computers and Graphics, 13(1989), 159-166.
[19]  A. Rosenfeld, Digital Topology, Amer. Math. Monthly, 86(1979), 76-87.
[20]  B. Samet, C. Vetro, P. Vetro, Fixed point theorem for α-ψ-contractive type mappings, Nonlinear Analysis 75 (2012), 2154-2165.
[21]  S. Z. Wang, B. Y. Li, Z. M. Gao, K. Iseki, Some fixed point theorems on expansion mappings, Math. Jpn. 29, 631-636, 1984.