Fixed Point Theorems in $ b$-Rectangular Metric Spaces

Year 2020, Volume: 3 Issue: 1, 28 - 32, 25.03.2020

Vildan Öztürk

https://doi.org/10.32323/ujma.609715

Cited By: 3

Abstract

The concept of $ b$-rectangular metric space is introduced as a generalization of $ b $-metric space and rectangular (generalized) metric space. In this paper, we introduce generalized almost contraction for two mappings and prove common fixed point theorems in $ b $-rectangular metric spaces.

Keywords

Almost contraction, $ b $-Rectangular metric, Fixed point

References

• [1] M. Abbas, D. Ilic, Common fixed points of generalized almost nonexpansive mappings, Filomat, 24 (2010), 11-18.
• [2] I. A. Bakhtin, The contraction mapping principle in almost metric spaces, In: Functional Analysis , 30 (1989), 26-34.
• [3] V. Berinde Approximating fixed points of weak F-contractions using the Picard iteration, Fixed Point Theory, 4 (2003), 131-142.
• [4] V. Berinde General constructive fixed point theorems for C´ iric´-type almost contractions in metric spaces, Carpathian J. Math., 24 (2008), 1-19.
• [5] A. Branciari, A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37.
• [6] S. Czerwik, Contraction mappings in b􀀀metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.
• [7] P. Das, A fixed point theorem in a generalized metric space, Soochow J. Math., 33 (2007), 33-39.
• [8] P. Das, B. K. Lahiri, Fixed point of a Ljubomir C´ iric´’s quasi-contraction mapping in a generalized metric space., Publ. Math. Debrecen, 61 (2001), 589-594.
• [9] H.S. Ding, V. Ozturk, S. Radenovi´c, On some new fixed point results in b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 378-386.
• [10] H.S. Ding, M. Imdad, S. Radenovic, J. Vujakovic, On some fixed point results in b-metric, rectangular and b-rectangular metric spaces, Arab Journal of Math. Sci., 22(2) (2016), 151-164.
• [11] R. George, S. Radenovi´c, K. P. Reshma, S. Shukla, Rectangular b-metric spaces and contraction principle, J. Nonlinear Sci. Appl., 8 (2015), 1005-1013.
• [12] R. George, R. Rajagopalan, Common fixed point results for $\psi -\varphi -$contractions in rectangular metric spaces, Bull. Math. Anal. Appl., 5 (2013), 44-52.
• [13] N. Goswami, N. Haokip, V. N. Mishra F-contractive type mappings in b metric spaces and some related fixed point results, Fixed Point Theory Appl., 2019 (2019), Article ID 13.
• [14] F. Gu, On some common coupled fixed point results in rectangular b-metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 4085-4098.
• [15] Z. Kadelburg, S. Radenovic, Fixed point results in generalized metric spaces without Hausdorff property, Math Sci., 8(125) (2014), doi:10.1007/s40096- 014-0125-6.
• [16] Z.D. Mitrovic, A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space, Mathematica Slovaca, 68(5) (2018), 1113-1116.
• [17] Z.D. Mitrovic, S. Radenovic, On Meir-Keeler contraction in Branciari b-metric spaces, https://www.researchgate.net/profile/Stojan Radenovic2/publication, (2018).
• [18] N. Mlaiki, N. Dedovic, H. Aydi, M. G. Filipoviac, B. Bin-Mohsin, S. Radenovic, Some New Observations on Geraghty and Ciric Type Results in b-Metric Spaces, Mathematics, 7 (2019), Article ID 643.
• [19] V. Özturk, S. Radenovic, Some remarks on b-(E.A)-property in b-metric spaces, Springerplus, 5 (2016), Article ID 544.
• [20] S. Radenovic, T. Dosenovic, V. Ozturk, C. Dolicanin, A note on the paper, Nonlinear integral equations with new admissibility types in b-metric spaces, J. Fixed Point Theory Appl., 19 (2017), 2287-2295.
• [21] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized $\left( \psi,\varphi \right) _{s}-$contractive mappings in ordered $b-$metric spaces. Fixed Point Theory Appl., 2013 (2013), Article ID 130.
• [22] J.R. Roshan, V. Parvaneh, Z. Kadelburg, N. Hussain, New fixed point results in b-rectangular metric spaces, Nonlinear Analysis: Modelling and Control, 21(5)(2016), 614–634.
• [23] D. Turkoglu, V. Ozturk, Common fixed point results for four mappings on partial metric spaces, Abstract Appl. Anal., 2012 (2012) Article ID 190862