Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces


In the present article, we study some fixed point theorems for a hybrid class of generalized contractive operators in the context of b-rectangular metric spaces. Examples justifying theorems and an open problem regarding to further generalizations for this type of operators are also given.


Cristian Daniel Alecsa
Babes-Bolyai University Faculty of Mathematics and Computer Sciences Cluj-Napoca, Romania
”Tiberiu Popoviciu” Institute of Numerical Analysis Romanian Academy Cluj-Napoca, Romania


Generalized contraction; b-rectangular metric space; expansive mappings; fixed point.

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Cristian-Daniel Alecsa, Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces, Stud. Univ. Babes-Bolyai Math. 62(2017), No. 4, 495–520 DOI: 10.24193/subbmath.2017.4.08


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[1] Aage, C.T., Salunke, J.N., Some fixed point theorems for expansion onto mappings on cone metric spaces, Acta Mathematica Sinica, English Series, 27(2011), no. 6, 1101-1106.

[2] Alghamdi, M.A., Hussain, N., Salimi, P., Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Ineq. Appl., 402(2013).

[3] Asadi, M., Some results of fixed point theorems in convex metric spaces, Nonlinear Func. Anal. Appl, 19(2014), no. 2, 171-175.

[4] Aydi, H., Karapinar, E., Moradi, S., Coincidence points for expansive mappings under c-distance in cone metric spaces, Int. Journal of Math. and Math. Sci., Vol. 2012, Art. ID 308921.

[5] Berinde, V., Pacurar, M., Stability of k-step fixed point iterative methods for some Presic type contractive mappings, J. Inequal. Appl., 149(2014).

[6] Branciari, A., A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57(2000), 31-37.

[7] Daheriya, R.D., Jain, R., Ughade, M., Some fixed point theorem for expansive type mapping in dislocated metric spaces, Internat. Sch. Research Network, ISRN Math. Analysis, Vol. 2012, Art. ID 376832, 5 pages.

[8] Ding, H.S., Ozturk, V., Radenovic, S., On some new fixed point results in b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8(2015), 378-386.

[9] George, R., Radenovic, S., Reshma, K.P., Shukla, S., Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., 8(2015), 1005-1013.

[10] Kadelburg, Z., Radenovic, S., Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci., 8(2014), 125.

[11] Kadelburg, Z., Radenovic, S., On generalized metric spaces: A survey, TWMS J. Pure Appl. Math., 5(2014), no. 1, 3-13.

[12] Kadelburg, Z., Radenovic, S., Pata-type common fixed point results in b-metric and b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8(2015), 944-954.

[13] Karapinar, E., Fixed point theorems in cone Banach spaces, Fixed Point Theory Appl.,  Art. ID 609281 (2009).

[14] Kumar, S., Garg, S.K., Expansion mapping theorems in metric spaces, Int. J. Contemp. Math. Sciences, 4(2009), no. 36, 1749-1758.

[15] Moosaei, M., Fixed point theorems in convex metric spaces, Fixed Point Theory Appl., 164(2012).

[16] Moosaei, M., Common fixed points for some generalized contraction pairs in convex metric spaces, Fixed Point Theory Appl., 98(2014).

[17] Moosaei, M., Azizi, A., On coincidence points of generalized contractive pair mappings in convex metric spaces, J. of Hyperstructures, 4(2015), no. 2, 136-141.

[18] Olaoluwa, H., Olaleru, J.O., A hybrid class of expansive-contractive mappings in cone b-metric spaces, Afr. Mat.

[19] Pathak, H.K., Some fixed points of expansion mappings, Internat. J. Math. and Math. Sci., 19(1996), no. 1, 97-102.

[20] Patil, S.R., Salunke, J.N., Fixed point theorems for expansion mappings in cone rectangular metric spaces, Gen. Math. Notes, 29(2015), no. 1, 30-39.

[21] Rashwan, R.A,m Some fixed point theorems in cone rectangular metric spaces, Math. Aeterna, 2(2012), no. 6, 573-587.

[22] Roshan, J.R., Hussain, N., Parvanhh, V., Kadelburg, Z., New fixed point results in rectangular b-metric spaces, Nonlinear Analysis: Modelling and Control, 21(2016), 21, no. 5, 614-634.

[23] Wang, C., Zhang, T., Approximating common fixed points for a pair of generalized nonlinear mappings in convex metric spaces, J. Nonlinear. Sci. Appl., 9(2016), 1-7.

[24] Zangenehmehr, P., Farajzadeh, A.P., Lashkaripour, P., Karamian, A., On fixed point theory for generalized contractions in cone rectangular metric spaces via scalarizing, Thai Journal of Math., 45(2012), no. 3, 717-724.

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