math. sci. appl. e-notes Mathematical Sciences and Applications E-Notes 2147-6268 Murat TOSUN 10.36753/mathenot.476779 Some Fixed Point Results on Complex Valued Sb-Metric Spaces https://orcid.org/0000-0002-4535-4019 Taş Nihal https://orcid.org/0000-0002-8152-1830 Özgür Nihal Yılmaz https://orcid.org/0000-0002-7986-886X Mlaiki Nabil 10 31 2018 6 2 10 21 12 21 2017 06 04 2018 Copyright © 2013, Mathematical Sciences and Applications E-Notes 2013 Mathematical Sciences and Applications E-Notes

More recently, the notion of a complex valued Sb-metric space has been introduced and studied. In thispaper, we investigate some basic properties of this new space. We study some fixed point results on acomplete complex valued Sb-metric space. A common fixed point theorem for two self-mappings on acomplete complex valued Sb-metric space is also given.

 Complex valued Sb-metric space fixed point common fixed point [1] Aghajani, A., Abbas, M. J. and Roshan, R., Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces, Filomat, 28(2014), no.6, 1087-1101. [2] An, T. V., Dung, N. V. and Hang, V. T. L., A new approach to fixed point theorems on G-metric spaces, Topology Appl., 160(2013), no.12, 1486-1493. [3] Azam, A., Fisher, B. and Khan, M., Common fixed point theorems in complex valued metric spaces, Number. Funct. Anal. Optim., 32(2011), 243-253. [4] Bakhtin, I. A., The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30(1989), 26-37. [5] Dubey, A. K., Shukla, R. and Dubey, R. P., Some fixed point theorems in complex valued b-metric spaces, Journal of Complex Systems, (2015), Article ID: 832467, 7 pages. [6] Dung, N. V., Hieu, N. T. and Radojevic, S., Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat, 28(2014), no.9, 1885-1898. [7] Ege, Ö., Complex valued Gb-metric spaces, J. Computational Analysis and Applications, 21(2016), no.2, 363-368. [8] Mlaiki, N. M., Common fixed points in complex S-metric space, Adv. Fixed Point Theory, 4(2014), no.4, 509-524. [9] Mlaiki, N. and Rohen, Y., Some coupled fixed point theorems in partially ordered Ab-metric space, J. Nonlinear Sci. Appl., 10(2017), 1731-1743. [10] Mohanta, S. K., Some fixed point theorems in G-metric spaces, An. ¸ Stiint. Univ. "Ovidius" Constanta Ser. Mat., 20(2012), no.1, 285-305. [11] Muhkeimer, A. A., Some common fixed point theorems in complex valued b-metric spaces, The Scientific Worl Journal, (2014) Article ID: 587825, 6 pages. [12] Mustafa, Z. and Sims, B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7(2006), no.2, 289-297. [13] Nashine, H. K., Imdad, M. and Hasan, M., Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl., 7(2014), 42-50. [14] Özgür, N. Y. and Ta¸s, N., Some fixed point theorems on S-metric spaces, Mat. Vesnik, 69(2017), no.1, 39-52. [15] Özgür, N. Y. and Ta¸s, N., Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Math. Sci., 11(2017), no.1, 7-16. [16] Özgür, N. Y. and Ta¸s, N., Some generalizations of fixed point theorems on S-metric spaces, Essays in Mathematics and Its Applications in Honor of Vladimir Arnold, New York, Springer, 2016. [17] Priyobarta, N., Rohen, Y. and Mlaiki, N., Complex valued Sb-metric spaces, J. Math. Anal., 8(2017), no.2, 13-24. [18] Rao, K. P. R., Swamy, P. R. and Prasad, J. R., A common fixed point theorem in complex valued b-metric spaces, Bulletin of Mathematics and Statistics Research, 1(2013), no.1. [19] Rohen, Y., Došenovi´c, T. and Radenovi´c, S., A note on the paper “a fixed point theorems in Sb-metric spaces”, Filomat, 31(2017), no.11, 3335-3346. [20] Sedghi, S., Shobe, N. and Aliouche, A., A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64(2012), no.3, 258-266. [21] Sedghi, S. and Dung, N. V., Fixed point theorems on S-metric spaces, Mat. Vesnik, 66(2014), no.1, 113-124. [22] Sedghi, S., Shobkolaei, N., Roshan, J. R. and Shatanawi, W., Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik, 66(2014), no.2, 190-201. [23] Sedghi, S., Gholidahneh, A., Došenovi´c, T., Esfahani, J. and Radenovi´c, S., Common fixed point of four maps in Sb-metric spaces, J. Linear Topol. Algebra, 5(2016), no.2, 93-104. [24] Souayah, N. and Mlaiki, N., A fixed point theorem in Sb-metric space, J. Math. Computer Sci., 16(2016), 131-139. [25] Ughade, M., Turkoglu, D., Singh, S. K. and Daheriya, R. D., Some fixed point theorems in Ab-metric space, British Journal of Mathematics & Computer Science 19(2016), no.6, 1-24. [26] Verma, R. K. and Pathak, H. K., Common fixed point theorems using property (E:A) in complex-valued metric spaces, Thai J. Math., 11(2013), no.2, 347-355.