Acknowledgement
The authors are grateful to the editor and anonymous referees for their comments and remarks to improve this manuscript.
References
- S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3(1) (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
- Y. I Alber, S. G. Delebriere, Principle of weakly contractive maps in Hilbert spaces, New results in operator theory and its applications, (1997), 7-22.
- BE. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Applications, 47(4), (2001), 2683-2693.
- Y. Song, Coincidence points for noncommuting f-weakly contractive mappings, International Journal of Computational and Applied Mathematics, 2(1), (2007), 51-58.
- Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contractions, Applied Mathematics Letters, 22(1), (2009), 75-78. https://doi.org/10.1016/j.aml.2008.02.007
- PN. Dutta and B. S Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications, 2008(1), (2008), 406368. https://doi.org/10.1155/2008/406368
- D. Doric, Common fixed point for generalized (ψ, φ)-weak contractions, Applied Mathematics Letters, 22(12), (2009), 1896-1900. https://doi.org/10.1016/j.aml.2009.08.001
- SMA. Aleomraninejad, Sh. Rezapour and N. Shahzad, Some fixed point results on a metric space with a graph, Topology and its Applications, 159(3), (2012), 659-663. https://doi.org/10.1016/j.topol.2011.10.013
- SMA. Aleomraninejad, Sh. Rezapour and N. Shahzad, Convergence of an iterative scheme for multifunctions, Journal of Fixed Point Theory and Applications, 12(1-2), (2012), 239-246. https://doi.org/10.1007/s11784-011-0046-z
- Asl. J. Hasanzade, Sh. Rezapour and N. Shahzad, On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory and Applications, 2012(1), (2102), 1-6. https://doi.org/10.1186/1687-1812-2012-1
- MA. Miandaragh, M. Postolache and Sh. Rezapour, Some approximate fixed point results for generalized α-contractive mappings, Sci. Bull.'Politeh.'Univ. Buchar., Ser. A, Appl. Math. Phys, 75(2), (2013), 3-10.
- BS. Choudhury and N. Metiya, The point of coincidence and common fixed point for a pair of mappings in cone metric spaces, Computers & Mathematics with Applications, 60(6), (2010), 1686-1695. https://doi.org/10.1016/j.camwa.2010.06.048
- B. D. Rouhani and S. Moradi, Common Fixed Point of Multi-valued Generalized ϕ-Weak Contractive Mappings, Fixed Point Theory and Appl, Fixed Point Theory and Applications, 10(2010), (2010), 708984.
- B. S. Choudhury, P. Konar, BE. Rhoades and N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Analysis: Theory, Methods & Applications, 74(6), (2011), 2116-2126. https://doi.org/10.1016/j.na.2010.11.017
- P. R. Agarwal, M. A. Alghamdi and N. Shahzad, Fixed point theory for cyclic generalized contractions in partial metric spaces, Fixed Point Theory and Applications, 2012(1), (2012), 40. https://doi.org/10.1186/1687-1812-2012-40
- D. Hui-Sheng, Z. Kadelburg, E. Karapinar and S. Radenovic, Common Fixed Points of Weak Contractions in Cone Metric Spaces, Abstract and Applied Analysis, 2012, (2012).
- CT. Aage and JN. Salunke, Fixed points of (ψ, φ)-weak contractions in cone metric spaces, Annals of Functional Analysis, 2(1), (2011), 59-71. https://doi.org/10.15352/afa/1399900262
- L-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of mathematical Analysis and Applications, 332(2), (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
- S. Gahler, 2-metrische Raume und ihre topologische Struktur, Mathematische Nachrichten, 26(1-4), (1963), 115-148. https://doi.org/10.1002/mana.19630260109
- B. Singh, S. Jain and P. Bhagat, Cone 2-metric space and fixed point theorem of contractive mappings, Commentationes Mathematicae, 52(2), (2012), 143-151.
- T. Wang, J. Yin and Q. Yan, Fixed point theorems on cone 2-metric spaces over Banach algebras and an application, Fixed point theory and applications, 2015(1), (2015), 204. https://doi.org/10.1186/s13663-015-0459-2
- M. Rangamma and P. Murthy, Hardy and Rogers type Contractive condition and common fixed point theorem in Cone 2-metric space for a family of self-maps, Global Journal of Pure and Applied Mathematics, 12(3), (2016), 2375-2383.
- P. Murthy and M. Rangamma, Fixed point theorems for convex contractions on cone 2-metric space over Banach algebra, Advances in Fixed Point Theory, 8(1), (2018), 83-97.
- G. Jungck, Compatible mappings and common fixed points, International Journal of Mathematics and Mathematical Sciences, 9(4), (1986), 771-779. https://doi.org/10.1155/S0161171286000935
- M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications, 341(1), (2008), 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070
- S. Jankovic, Z. Kadelburg, S. Radenovic and BE. Rhoades, Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces, Fixed Point Theory and Applications, 2009(1), (2009), 761086. https://doi.org/10.1155/2009/761086
- J. Jachymski, Order-theoretic aspects of metric fixed point theory, Handbook of metric fixed point theory, (2001), 613-641.
- K. Deimling, Nonlinear functional analysis, Courier Corporation, (2010).