Coincidence points and common fixed points for hybrid pair of mappings in b-metric spaces endowed with a graph

Subject Areas : Fixed point theory

S. K. Mohanta ¹ (Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India)
S. Patra ² (Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India)

Received: 2017-10-30 Accepted : 2017-12-23 Published : 2017-12-01

Keywords:

References:

[1] M. U. Ali, T. Kamran, E. Karapinar, (α, ψ, ξ)-contractive multivalued mappings, Fixed Point Theory Appl. (2014), 2014:7.

[2] S. Aleomraninejad, S. Rezapour, N. Shahzad, Fixed point results on subgraphs of directed graphs, Mathe- matical Sciences. (2013), 7:41.

[3] J. H. Asl, S. Rezapour, N. Shahzad, On fixed points of α−ψ-contractive multifunctions, Fixed Point Theory and Appl. (2012), 2012:212.

[4] M. R. Alfuraidan, M. A. Khamsi, Caristi fixed point theorem in metric spaces with a graph, Abstr. Appl. Anal. (2014), 2014:303484.

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

[6] S. Banach, Sur les ope´rations dans les ensembles abstraits et leur application aux equations inte´grales, Fund. Math. 3 (1922), 133-181.

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

[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.

[9] F. Bojor, Fixed point of φ-contraction in metric spaces endowed with a graph, Anal of the University of Cralova, Math. Comput. Sci. Series. 37 (2010), 85-92.

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

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

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

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

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

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

[16] K. Fallahi, G. Soleimani Rad, Fixed point results in cone metric spaces endowed with a graph, Sahand Communications in Mathematical Analysis. 6 (2017), 39-47.

[17] K. Fallahi, M. Abbas, G. Soleimani Rad, Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results, Appl. Gen. Topol. 18 (2017), 391-400.

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

[19] N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in α-complete metric spaces with applications, Abstr. Appl. Anal. (2014), 2014:280817.

[20] N. Hussain, R. Saadati, R. P. Agrawal, On the topology and wt-distance on metric type spaces, Fixed Point Theory Appl. (2014), 2014:88.

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

[22] H. Kaneko, S. Sessa, Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci. 12 (1989), 257-262.

[23] P. Kaushik, S. Kumar, Fixed point results for (α, ψ, ξ)-contractive compatible multi-valued mappings, J. Nonlinear Anal. Appl., doi:10.5899/2016/jnaa-00305.

[24] M. A. Kutbi, W. Sintunavarat, On new fixed point results for (α, ψ, ξ)-contractive multi-valued mappings on α-complete metric spaces and their consequences, Fixed Point Theory Appl. (2015), 2015:2.

[25] S. K. Mohanta, Common fixed points in b-metric spaces endowed with a graph, Matematicki Vesnik. 68 (2016), 140-154.

[26] S. K. Mohanta, Coincidence points and common fixed points for expansive type mappings in b-metric spaces, Iran. J. Math Sci. Infor. 11 (2016), 101-113.

[27] S. Nadler, Multi-valued contraction mappings, Pac. J. Math. 20 (1969), 475-488.

[28] H. K. Pathak, Fixed point theorems for weak compatible multi-valued and single-valued mappings, Acta. Math. Hungar. 67 (1995), 69-78.

[29] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized (ψ, φ)s-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl. (2013), 2013:159.

[30] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α − ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.

[31] J. Tiammee, S. Suantal, Coincidence point theorems for graph-preserving multi-valued mappings, Fixed Point Theory Appl. (2014), 2014:70.