Volume 65 | Issue 11 | Year 2019 | Article Id. IJMTT-V65I11P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I11P509

This paper consists of some coupled and common coupled fixed point theorems in vector b-metric spaces. Vector b-metric space or E-b-metric space was introduced by Petre [6] merging the concepts of vector metric space as introduced by Cevik [4] and b-metric space as introduced by Czerwik [5]. We generalize the results of Shatnanawi and Hani [8] and Rao et al. [7].

[1] S. Agarwal, K. Qureshi, J.Nema, A fixed point theorem for b-metric space, International Journal of Pure and Applied Mathematical Sciences, 945-50, 2016.

[2] C.D. Aliprantis, K.C. Border, Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1999.

[3] I.A.Bakhtin, The contraction mapping principle in quasi-metric spaces, Functional Analysis, 30, 26-37, 1989.

[4] Cevik, I. Altun, Vector metric spaces and some properties, Topol. Method Nonl. An., 34, 375-382, 2009.

[5] S.Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostrviensis, 1, 5-11, 1993.

[6] I.R.Petre, Fixed point theorems in E-b-metric spaces, J. Nonlinear Sci. App., 7, 264-271, 2014.

[7] K.P.R. Rao, K.R.K.Rao, V.C.C.Raju, A Suzuki type unique common coupled fixed point theorem in metric spaces, International Journal of Innovative Research in Science, Engineering and Technology, 2, 5187-5192, 2013.

[8] W. Shatanawi, M.B.Hani, A coupled fixed point theorem in b-metric spaces, International Journal of Pure and Applied Mathematics, vol. 19, 4, 889-897, 2016.

[9] I.Altun, A.Erduran, A Suzuki type fixed point theorem, Internat. Math. Math. Sci., vol. 2011, article ID 736063, 9, 2011.

[10] W. Shatanawi, Coupled fixed point theorems in generalized metric spaces, Hacettepe Journal of Mathematics and Statistics, vol . 40, 3441-447, 2011.

[11] W.Shatanawi, B.Samet, M.Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Mathematical and Computer Modelling, 55, 680-687, 2012.

[12] T. Bhakar, V. Lakshmikanthan, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65, 1379- 1393, 2006.

[13] Y.J. Cho, Z. Kadeelburg, R. Saadati, W.Shatanawi, Coupled fixed theorems under weak contractions, Discrete Dyanamics in Nature and Society 2012.

[14] V. Lakshmikantham, L.B. Ciric , Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces , Nonlinear Anal., 70, 2009.

[15] I.Altun, C.Cevik, Some common fixed point theorems in vector metric spaces, Filomat, 25:1, 105-113, 2011.

[16] C.Cevik, On continuity of functions between vector metric spaces, Hindawi Pub. Corporation, J.Funct. Space, 1-6, 2014.

Mamta Kamra, Rahul Hooda, Archana Malik, "Coupled Fixed Point Theorems in Vector b-metric Space," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 65, no. 11, pp. 83-98, 2019. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V65I11P509