Geodesic
Almost monotone contractions on weighted graphs
Alfuraidan, Monther R.1 ; Bachar, Mostafa2 ; Khamsi, Mohamed A.3
1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2 Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia
3 Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U. S. A.
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5189-5195.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Almost contraction mappings were introduced as an extension to the contraction mappings for which the conclusion of the Banach contraction principle (BCP in short) holds. In this paper, the concept of monotone almost contractions defined on a weighted graph is introduced. Then a fixed point theorem for such mappings is given.
DOI : 10.22436/jnsa.009.08.04
Classification : 47H10, 47H09, 46B20
Keywords: Almost contraction, directed graph, fixed point, monotone mapping, multivalued mapping.

Alfuraidan, Monther R. 1 ; Bachar, Mostafa 2 ; Khamsi, Mohamed A. 3

1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2 Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia
3 Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U. S. A. 
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Alfuraidan, Monther R.; Bachar, Mostafa; Khamsi, Mohamed A. Almost monotone contractions on weighted graphs. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5189-5195. doi : 10.22436/jnsa.009.08.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.08.04/

[1] M. R. Alfuraidan Remarks on monotone multivalued mappings on a metric space with a graph, J. Inequal. Appl., Volume 2015 (2015), pp. 1-7

[2] Banach, S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., Volume 3 (1922), pp. 133-181

[3] Berinde, V. On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., Volume 19 (2003), pp. 7-22

[4] Berinde, V.; Păcurar, M. Fixed points and continuity of almost contractions, Fixed Point Theory, Volume 9 (2008), pp. 23-34

[5] S. K. Chatterjea Fixed-point theorems, C. R. Acad. Bulgare Sci., Volume 25 (1972), pp. 727-730

[6] El-Sayed, S. M.; A. C. M. Ran On an iteration method for solving a class of nonlinear matrix equations , SIAM J. Matrix Anal. Appl., Volume 23 (2002), pp. 632-645

[7] Feng, Y.; Liu, S. Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., Volume 317 (2006), pp. 103-112

[8] Goebel, K.; Kirk, W. A. Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1990

[9] Goodrich, M. T.; Tamassia, R. Algorithm design: foundations, analysis and internet examples, John Wiley & Sons, Inc., New York, 2001

[10] Jachymski, J. The contraction principle for mappings on a metric space with a graph , Proc. Amer. Math. Soc., Volume 136 (2008), pp. 1359-1373

[11] Kannan, R. Some results on fixed points, Bull. Calcutta Math. Soc., Volume 60 (1968), pp. 71-76

[12] Khamsi, M. A.; W. A. Kirk An introduction to metric spaces and fixed point theory, Pure and Applied Mathematics, Wiley-Interscience, New York, 2001

[13] Klim, D.; Wardowski, D. Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., Volume 334 (2007), pp. 132-139

[14] Nadler, S. B. Multi-valued contraction mappings, Pacific J. Math., Volume 30 (1969), pp. 475-488

[15] Nieto, J. J.; Rodríguez-López, R. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, Volume 22 (2005), pp. 223-239

[16] Ran, A. C. M.; Reurings, M. C. B. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., Volume 132 (2004), pp. 1435-1443

[17] Rus, I. A. Generalized contractions, Seminar on Fixed Point Theory, 3 (1983), 1-130, Preprint, 83-3, Univ. ''Babe-Bolyai'', Cluj-Napoca, 1983

[18] Rus, I. A. Generalized contractions and applications, Cluj University Press, Cluj-Napoca, 2001

[19] Tasković, M. R. Osnove teorije fiksne take, (Serbo-Croatian) [Foundations of fixed-point theory] With an English summary, Matematicka Biblioteka [Mathematical Library], Zavod za Udzbenike i Nastavna Sredstva, Belgrade, Volume 1986 (1986), pp. 1-272

[20] Turinici, M. Fixed points for monotone iteratively local contractions, Demonstratio Math., Volume 19 (1986), pp. 171-180

[21] Udo-utun, X. A.; Siddiqui, Z. U.; Balla, M. Y. An extension of the contraction mapping principle to Lipschitzian mappings, Fixed Point Theory Appl., Volume 2015 (2015), pp. 1-7

[22] D. W. Wallis A beginner's guide to graph theory , Second edition, Birkhäuser Boston, Inc., Boston, 2007

[23] Zamfirescu, T. Fix point theorems in metric spaces, Arch. Math. (Basel), Volume 23 (1972), pp. 292-298

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