Document Type: Research Paper

Authors

1 Department of Mathematics‎, COMSATS University‎, ‎chak shahzad‎, ‎Islamabad‎, ‎44,000‎, ‎Pakistan

2 Department of Mathematics‎, ‎Faculty of Physical Sciences‎, ‎Ahmadu Bello University‎, ‎Nigeria

Abstract

‎The aim of this paper is to establish and prove some results on common fixed point‎ for a pair of multi-valued mappings in complex valued $b$-metric spaces‎. ‎Our‎ ‎results generalize and extend a few results in the literature‎.
 

Keywords

Main Subjects

[1] J. Ahmad, C. Klin-Eam, A. Azam, Common fixed points for multivalued mappings in complex valued metric spaces with applications, Abs. Appl. Anal. 2013, 1:12.
[2] J. Ahmad, N. Hussain, A. Azam, M. Arshad, Common fixed point results in complex valued metric with
application to system of integral equations, J. Nonlear Convex. Anal. 29 (5) (2015), 855-871.
[3] S. Aleksic, Z. Kadelburg, Z. D. Mitrovic, S. Radenovic, A new survey: cone metric spaces, J. Inter. Math. Virtual Institute. 9 (2019), 93-121.
[4] A. Azam, J. Ahmad, P. Kumam, Common fixed point theorems for multi-valued mappings in complex-valued metric spaces, J. Inequl. Appl. 2013, 2013:578.
[5] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 32 (3) (2011), 243-253.
[6] A. Azam, N. Mehmood, Multivalued fixed point theorems in tvs-cone metric spaces, Fixed Point Theory Appl. 2013, 2013:184.
[7] A. Azam, M. Shakeel, Weakly contractive maps and common fixed points, Mat. Vesnik. 60 (2) (2008), 101-106.
[8] S. Banach, Sur les operation dans les ensembles abstraits et applications aux equations integrales, Fund. Math. 3 (1922), 133-181.
[9] I. A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal. 30 (1989), 26-37.
[10] M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2) (2007), 772-782.
[11] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251.
[12] S. K. Chatterjea, Fixed point theorem, C.R. Acad. Bulgare Sci. 25 (1972), 727-730.
[13] B. K. Dass, S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (12) (1975), 1455-1458.
[14] A. K. Dubey, Common fixed point results for contractive mappings in complex valued b-metric spaces, Nonlinear Funct. Anal. Appl. 20 (2015), 257-268.
[15] A. K. Dubey, R. Shukla, R. P. Dubey, Some fixed point theorems in complex valued b-metric spaces, J. Complex Systems. 2015, 2015:832467.
[16] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math Soc. 1 (1) (1967), 74-79.
[17] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2) (2007), 1468-1476.
[18] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (2) (1977), 223-230.
[19] S. Jankovic, Z. Golubovic, S. Radenovic, Compatible and weakly compatible mappings in cone metric spaces, Math. Comput. Model. 52 (9-10) (2010), 1728-1738.
[20] R. Kannan, Some results on fixed points, Bull Calcutta Math. Soc. 60 (1968), 71-76.
[21] J. Kumar. Common fixed point theorem for generalized contractive type maps on complex valued b-metric spaces, Inter. J. Math. Anal. 9 (2015), 2327-2334.
[22] N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1) (1989), 177-188.
[23] A. A. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces, The Scientific World J. 2014, 2014:587825.
[24] S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (2) (1969), 475-488.
[25] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.
[26] R. P. Rao, J. R. Swamy, J. R. Prasad, A common fixed point theorem in complex valued b-metric spaces, Bull. Math. Statis. Research. 1 (2013), 1-8.
[27] W. Shatanawi, V. C. Rajic, S. Radenovic, A. Al-Rawashdeh, Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces, Fixed Point Theory Appl. 2012, 1:106.