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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.20 no.1 Temuco mar. 2018

http://dx.doi.org/10.4067/S0719-06462018000100041 

Articles

Common Fixed Point Results in C -Algebra Valued b-Metric Spaces Via Digraphs

Sushanta Kumar Mohanta1 

1West Bengal State University, Department of Mathematics, Barasat, 24 Parganas (North), West Bengal, Kolkata 700126, India. smwbes@yahoo.in

Abstract

We discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings defined on a C-algebra valued b-metric space endowed with a graph. Our results extend and supplement several recent results in the literature. Strength of hypotheses made in the first result have been weighted through illustrative examples.

Resumen

Discutimos la existencia y unicidad de puntos de coincidencia y puntos fijos comunes para un par de aplicaciones definidas en un b-espacio métrico a valores en una álgebra C* dotado de un grafo en sí mismo. Nuestros resultados extienden y suplementan diversos resultados recientes en la literatura. La fuerza de las hipótesis impuestas al primer resultado se evalúa a través de ejemplos ilustrativos.

Keywords and Phrases: C∗-algebra; C∗-algebra valued b-metric; directed graph; C∗-algebra valued G-contraction; common fixed point.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

References

[1] A. Aghajani, M. Abbas and J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64, 2014, 941-960. [ Links ]

[2] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341, 2008, 416-420. [ Links ]

[3] M. R. Alfuraidan, M. A. Khamsi, Caristi fixed point theorem in metric spaces with a graph, Abstract and Applied Analysis, vol. 2014, Article ID 303484. [ Links ]

[4] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst. Unianowsk, 30, 1989, 26-37. [ Links ]

[5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3, 1922, 133-181. [ Links ]

[6] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4, 2009, 285-301. [ Links ]

[7] J. A. Bondy and U. S. R. Murty, Graph theory with applications, American Elsevier Publishing Co., Inc., New York, 1976. [ Links ]

[8] I. Beg, A. R. Butt, S. Radojevic, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60, 2010, 1214-1219. [ Links ]

[9] F. Bojor, Fixed point of ϕ-contraction in metric spaces endowed with a graph, Annala of the University of Cralova, Mathematics and Computer Science Series, 37, 2010, 85-92. [ Links ]

[10] F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. St. Univ. Ovidius Constanta, 20, 2012, 31-40. [ Links ]

[11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav, 1, 1993, 5-11. [ Links ]

[12] G. Chartrand, L. Lesniak, and P. Zhang, Graph and digraph, CRC Press, New York, NY, USA, 2011. [ Links ]

[13] M. Cosentino, P. Salimi, P. Vetro, Fixed point results on metric-type spaces, Acta Math. Sci. Ser. B Engl. Ed., 34, 2014, 1237-1253. [ Links ]

[14] R. Douglas, Banach algebra techniques in operator theory, Springer, Berlin, 1998. [ Links ]

[15] F. Echenique, A short and constructive proof of Tarski’s fixed point theorem, Internat. J. Game Theory, 33, 2005, 215-218. [ Links ]

[16] R. Espinola and W. A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153, 2006, 1046-1055. [ Links ]

[17] J. I. Gross and J. Yellen, Graph theory and its applications, CRC Press, New York, NY, USA, 1999. [ Links ]

[18] N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012, 2012:126, doi:10.1186/1687-1812-2012-126. [ Links ]

[19] G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci., 4, 1996, 199-215. [ Links ]

[20] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136, 2008, 1359-1373. [ Links ]

[21] Z. Ma, L. Jiang, C-algebra-valued b-metric spaces and related fixed point theorems, Fixed Point Theory and Applications, 2015, 2015:222. [ Links ]

[22] Z. Ma, L. Jiang and H. Sun , C-algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory and Applications , 2014, 2014:206. [ Links ]

[23] G. Murphy, C-Algebra and operator theory, Academic Press, London, 1990. [ Links ]

[24] S. K. Mohanta, Some Fixed Point Theorems in Cone Modular Spaces with a Graph, Bolletino dellUnione Matematica Italiana, 2016, DOI 10.1007/s40574-016-0086-9. [ Links ]

[25] S. K. Mohanta, Some fixed point theorems using wt-distance in b-metric spaces, Fasciculi Mathematici, no. 54, 2015, 125-140. [ Links ]

[26] J. J. Nieto and R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, Englosh Ser., 2007, 2205-2212. [ Links ]

[27] D. Reem, S. Reich, A. J. Zaslavski, Two results in metric fixed point theory, J. Fixed Point Theory Appl. , 1, 2007, 149-157. [ Links ]

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