Application of Fixed Point Theorems for Digital Contractive Type Mappings in Digital Metric Space

Neena Gupta¹ , Amardeep Singh² , Geeta Modi³

Section:Survey Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.323-327, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.323327

Online published on Feb 28, 2019

Copyright © Neena Gupta, Amardeep Singh, Geeta Modi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

466 Views    268 Downloads    74 Downloads

Abstract :
In this paper we introduce a notion and define a contractive type mapping for digital metric spaces. We prove some fixed point theorems in digital metric space by using contractive type mapping. We obtain Banach contraction principle in digital metric space. The purpose of this paper is to associate fixed point theory and digital images. This shows an application of fixed point theory in digital metric space.

Key-Words / Index Term :
digital image, digital metric space, Banach contraction principle, finite sequence, increasing sequence, decreasing sequence, θ-contractive.

References :
[1] Banach S,“Sur les operations dans les ensembles abstraits et leurs applications aux equations integrals”,Fund. Math., No. 3, pp. 133–181, 1922.
[2] Brouwer LEJ, “ubereineindeutige,stetiger Transformation envon Flaachen in Sich”, Math. Ann., 69, pp. 176-180, 1910.
[3] Brouwer LEJ,“uberAbbildungen Von Mannigfaltigkeiton”, Math. Ann., 77,pp. 97-115, 1912.
[4] Kong TY, “A Digital Fundamental Group, Computers and Graphics”, 13, pp. 159-166, 1989.
[5] Boxer L, “Digitally Continuous Functions”,Pattern Recognition Letters, 15, pp. 833- 839, 1994.
[6] Boxer L, “A Classical Constructions for The Digital Fundamental Group”, J.Math. Imaging Vis., 10, pp. 51-62,1999.
[7] Boxer L, “Properties of Digital Homotopy”, J. Math. Imaging Vis., 22,pp. 19-26, 2005.
[8] Rosenfeld A,“Continuous functions on digital pictures”, Pattern Recognition Letters 4, pp. 177-184, 1986.
[9] Ege O, Karaca I, “Applications of The Lefschetz Number to Digital Images”,Bull. Belg. Math. Soc. Simon Stevin,21,pp.823-839,2014.
[10] Ege O, Karaca I, “Banach Fixed Point Theorem for Digital Images”, J. Nonlinear Sci. Appl. 8, pp. 237-245, 2015.
[11] Ege O, Karaca I, “Lefschetz Fixed Point Theorem for Digital Images”,Fixed Point Theory, Appl., 13 pages, 2013.
[12] Han S.E,“Non-Product property of the digital fundamental group”, Inform. Sci., 171, pp. 73-91, 2005.
[13] Rosenfeld A, “Digital Topology”,Amer. Math. Monthly, 86, pp. 76-87,1979.
[14] Han S. E, “Banach fixed point Theorem from the viewpoint of digital topology”, J. Nonlinear sci. Appl., 9, pp. 895-905, 2016.
[15] Sridevi K., M. V. R. Kameshwari And D. M. K. Kiran,“Fixed Point Theorem for Digital Contractive Type Mappings in Digital Metric Space” International
Journal of Mathematics Trends and Technology, Vol. 48, No. 3, pp. 159-167, 2017