Common fixed point theorems of integral type in G-metric space via control function

Document Type : Research Paper


Department of Mathematics, K.R.M.D.A.V. College, Nakodar-144040, Punjab, India


In this paper, we establish fixed point results for two pairs of functions with the assistance of CLR property in the context of $\mathcal{G}$-metric space. Our sequel generalizes various existing fixed-point results that are given in the literature. An illustrative example is likewise given to demonstrate that our speculation from metric space to $\mathcal{G}$-metric spaces is genuine.


[1] S. Arora, M. Kumar and S. Mishra, A new type of coincidence and common fixed-point theorems for modified α-admissible Z-contraction via simulation function, J. Math. Fund. Sci. 52 (2020), no. 1, 27–42.
[2] S. Arora, Common fixed point theorems satisfying common limit range property in the frame of Gs metric spaces, Math. Sci. Lett. 10 (2021), no. 2, 1–5.
[3] H. Aydi, S. Chauhan and S. Radenovi, Fixed point of weakly compatible mappings in G-metric spaces satisfying common limit range property, Ser. Math. Inf. 28 (2013), no. 2, 197–210.
[4] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), 531–536.
[5] P. Debnath, Z.D. Mitrovic and S.Y. Cho, Common fixed points of Kannan, Chatterjea and Reich type pairs of self-maps in a complete metric space, Sao Paulo J. Math. Sci. 15 (2021), 383–391.
[6] A. Djoudi and F. Merghadi, Common fixed point theorems for maps under a contractive condition of integral type, J. Math. Anal. Appl. 341 (2012), 953–960.
[7] F. Khojasteh, Z. Goodarzi and A. Razani, Some fixed point theorems of integral type contraction in cone metric spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 189684, 1–10.
[8] M. Kumar, S. Arora, M. Imdad and W.M. Alfaqih, Coincidence and common fixed point results via simulation-functions in G-metric spaces, J. Math. Comput. Sci. 19 (2019), 288–300.
[9] M. Kumar, S. Arora and S. Mishra, On the power of simulation map for almost Z-contraction in G-metric space with applications to the solution of the integral equation, Ital. J. Pure Appl. Math. 44 (2020), 639–648.
[10] Z. Liu, X. Li, S. Kang and S. Cho, Fixed point theorems for mappings satisfying contractive conditions of integral type and applications, Fixed Point Theory Appl. 2011 (2011), Article ID 64, 1-9.
[11] S. Manro, S.S. Bhatia, S. Kumar and C. Vetro, A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A, Fixed Point Theory Appl. 41 (2013), no. 2, 1–9.
[12] P. Murthy, S. Kumar and K. Tas, Common fixed points of self maps satisfying an integral type contractive condition in fuzzy metric spaces, Math. Commun. 15 (2010), 521–537.
[13] P.P. Murthy, Z. Mitrovic, C.P. Dhuri and S. Radenovic, The common fixed points in a bipolar metric space, Gulf J. Math. 12 (2022), no. 2 31–38.
[14] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), no. 2, 289–297.
[15] Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl. 2008 (2008), Article ID 189870, 1–12.
[16] S.K. Panda, B. Alamri, N. Hussain and S. Chandok, Unification of the fixed point in integral type metric spaces, Symmetry 732 (2018), no. 10, 1–21.
[17] M. Rahman, M. Sarwar and M. Rahman, Fixed point results of Altman integral type mappings in S-metric spaces, Int. J. Anal. Appl. 10 (2016), no. 1, 58–63.
[18] B. Samet, C. Vetro and P. Vetro, Fixed point theorem for α-contractive type mappings, Nonlinear Anal. 75 (2012), 2154–2165.
[19] M. Sarwar, M.B. Zada and I.M. Erhan, Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations, Fixed Point Theory Appl. 217 (2015), 1–15.
[20] W. Sintunavarat and P. Kumam, Gregus-type common fixed point theorems for tangential multi-valued mappings
of integral type in metric spaces, Int. J. Math. Math. Sci. 2011 (2011), Article ID 923458, 1–9.
Volume 14, Issue 8
August 2023
Pages 343-350
  • Receive Date: 03 October 2022
  • Revise Date: 01 February 2023
  • Accept Date: 10 February 2023
  • First Publish Date: 14 February 2023