Fixed Point Theorems for Four Mappings in a Complete Digital Metric Space
Resumo
We demonstrate a fixed-point theorem for digital photographs in this study. In particular, we prove a special digital fixed-point theorem for four self-mappings in an entire digital metric space. In the setting of digital metric space, our solution is a logical progression of the seminal work of Bhagwat and Singh [2].
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Referências
1. Banach, S. Sur les oprations dans les ensembles abstraits et leurs applications aux quations intgrales, Fund. Math., 3,
133–181, (1922).
2. Bhagwat, N. and Singh, B., Fixed points of a pair of mappings, Indian J. Pure Appl. Math., 178, 994-997, (1986).
3. Bertrand, G., Simple points, topological numbers and geodesic neighbourhoods in cubic grids, Pattern Recognition
Letters, 15, 1003-1011, (1994).
4. Bertrand, G. and Malgouyres, M., Some topological properties of discrete surfaces in Z3, J. Math. Imaging Vis., 11,
207-221, (1999).
5. Boxer, L. A classical construction for the digital fundamental group, J. Math. Imaging Vis., 10, 51-62, (1999).
6. Brown, R. The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., (1971).
7. Das, K. B. and Gupta, S. Fixed point theorems, Indian J. Pure Appl. Math., 10, 886-889, (1979).
8. Ege, O. and Karaca, I., Lefschetz fixed point theorem for digital images, Fixed Point Theory Appl., 253, 1-13, (2013).
9. Ege, O. and Karaca, I., Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl., 8, 1-9, (2015).
10. Han, E. S., Non-product property of the digital fundamental group, Inform. Sci., 171, 73-91, (2005).
11. Han, E. S., On the simplicial complex stemmed from a digital graph, Honam Math. J., 27, 115-129, (2005).
12. Han, E. S., Connected sum of digital closed surfaces,” Inform. Sci., 176, 332-348, (2006).
13. Han, E. S., Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Inform. Sci., 176, 120–134,
(2006).
14. Han, E. S., Continuities and homeomorphisms in computer topology and their applications, J. Korean Math. Soc., 45,
923-952, (2008).
15. Han, E. S., KD-(k0,k1)-homotopy equivalence and its applications, J. Korean Math. Soc., 47, 1031–1054, (2010).
16. Han, E. S., Digital version of the fixed point theory, Proc. 11th ICFPTA (Abstracts), (2015).
17. Jain, S. and Jain, B. L. On Banach contraction principle in a cone metric space, J. Nonlinear Sci. Appl., 5, 252-258,
(2012).
18. Jleli, M. and Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., (2014), 8 pages.
19. Kong, Y. T. and Rosenfeld, A., Topological Algorithms for Digital Image Processing, Elsevier Science, Amsterdam,
(1996).
20. Malgouyres, R., Computing the fundamental group in digital spaces, Int. J. Pattern Recogn. Artif. Intell., 15, 1075-1088,
(2001).
21. Malgouyres, R. and Bertrand, G., A new local property of strong n-surfaces, Pattern Recognition Letters, 20, 417-428,
(1999).
22. Merryfield, J., A generalization of the Banach contraction principle, J. Math. Anal. Appl., 273, 112-120, (2002).
23. Palais, S. R., A simple proof of the Banach contraction principle, J. Fixed Point Theory Appl., 2, 221-223, (2007).
24. Pathak, K. H, A note on fixed point theorems of Rao and Rao, Bull. Cal. Math., 79, 267-273, (1987).
25. Rosenfeld, A., Digital topology, Amer. Math. Monthly, 86, 621-630, (1979).
26. Rosenfeld, A. Continuous functions on digital pictures, Pattern Recognition Letters, 4, 177-184, (1986).
27. Shatanawi, W. and Nashine, K. H., A generalization of Banach’s contraction principle for nonlinear contraction in a
partial metric space, J. Nonlinear Sci. Appl., 5, 37-43, (2012).
28. Slapal, J., Topological structuring of the digital plane, Discrete Math. Theor. Comput. Sci., 15, 165-176, (2013).
29. Wyse, F. and Marcus, D., Solution to problem 5712, Amer. Math. Monthly, 77, 1119, (1970).
133–181, (1922).
2. Bhagwat, N. and Singh, B., Fixed points of a pair of mappings, Indian J. Pure Appl. Math., 178, 994-997, (1986).
3. Bertrand, G., Simple points, topological numbers and geodesic neighbourhoods in cubic grids, Pattern Recognition
Letters, 15, 1003-1011, (1994).
4. Bertrand, G. and Malgouyres, M., Some topological properties of discrete surfaces in Z3, J. Math. Imaging Vis., 11,
207-221, (1999).
5. Boxer, L. A classical construction for the digital fundamental group, J. Math. Imaging Vis., 10, 51-62, (1999).
6. Brown, R. The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., (1971).
7. Das, K. B. and Gupta, S. Fixed point theorems, Indian J. Pure Appl. Math., 10, 886-889, (1979).
8. Ege, O. and Karaca, I., Lefschetz fixed point theorem for digital images, Fixed Point Theory Appl., 253, 1-13, (2013).
9. Ege, O. and Karaca, I., Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl., 8, 1-9, (2015).
10. Han, E. S., Non-product property of the digital fundamental group, Inform. Sci., 171, 73-91, (2005).
11. Han, E. S., On the simplicial complex stemmed from a digital graph, Honam Math. J., 27, 115-129, (2005).
12. Han, E. S., Connected sum of digital closed surfaces,” Inform. Sci., 176, 332-348, (2006).
13. Han, E. S., Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Inform. Sci., 176, 120–134,
(2006).
14. Han, E. S., Continuities and homeomorphisms in computer topology and their applications, J. Korean Math. Soc., 45,
923-952, (2008).
15. Han, E. S., KD-(k0,k1)-homotopy equivalence and its applications, J. Korean Math. Soc., 47, 1031–1054, (2010).
16. Han, E. S., Digital version of the fixed point theory, Proc. 11th ICFPTA (Abstracts), (2015).
17. Jain, S. and Jain, B. L. On Banach contraction principle in a cone metric space, J. Nonlinear Sci. Appl., 5, 252-258,
(2012).
18. Jleli, M. and Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., (2014), 8 pages.
19. Kong, Y. T. and Rosenfeld, A., Topological Algorithms for Digital Image Processing, Elsevier Science, Amsterdam,
(1996).
20. Malgouyres, R., Computing the fundamental group in digital spaces, Int. J. Pattern Recogn. Artif. Intell., 15, 1075-1088,
(2001).
21. Malgouyres, R. and Bertrand, G., A new local property of strong n-surfaces, Pattern Recognition Letters, 20, 417-428,
(1999).
22. Merryfield, J., A generalization of the Banach contraction principle, J. Math. Anal. Appl., 273, 112-120, (2002).
23. Palais, S. R., A simple proof of the Banach contraction principle, J. Fixed Point Theory Appl., 2, 221-223, (2007).
24. Pathak, K. H, A note on fixed point theorems of Rao and Rao, Bull. Cal. Math., 79, 267-273, (1987).
25. Rosenfeld, A., Digital topology, Amer. Math. Monthly, 86, 621-630, (1979).
26. Rosenfeld, A. Continuous functions on digital pictures, Pattern Recognition Letters, 4, 177-184, (1986).
27. Shatanawi, W. and Nashine, K. H., A generalization of Banach’s contraction principle for nonlinear contraction in a
partial metric space, J. Nonlinear Sci. Appl., 5, 37-43, (2012).
28. Slapal, J., Topological structuring of the digital plane, Discrete Math. Theor. Comput. Sci., 15, 165-176, (2013).
29. Wyse, F. and Marcus, D., Solution to problem 5712, Amer. Math. Monthly, 77, 1119, (1970).
Publicado
2026-02-21
Seção
Special Issue: Non-Linear Analysis and Applied Mathematics
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