Solutions of integral equations via fixed point results in extended Branciari b-distance spaces

Document Type : Research Paper


VIT Bhopal University, Mathematics Division, SASL, India


In this work, we prove the existence of the solution of integral equations via fixed point results in the framework of extended Branciari $b$-distance spaces. In order to do this, we introduce ${FG}$-contractive conditions in extended Branciari $b$-distance spaces and derive common fixed points results for triangular $\alpha$-admissible mappings, followed by some suitable examples.


[1] T. Abdeljawad, E. Karapinar, S. Kumari Panda and N. Mlaiki, Solutions of boundary value problems on extendedbranciari b-distance, J. Inequal. Appl. 2020 (2020), no. 1, 1–16.
[2] A.A. Abdou and M.F.S. Alasmari, Fixed point theorems for generalized α-ψ-contractive mappings in extended
b-metric spaces with applications, AIMS Math. 6 (2021), no. 6, 5465–5478.
[3] E. Ameer, H. Huang, M. Nazam and M. Arshad, Fixed point theorems for multivalued γ-fg-contractions with (α,
β)-admissible mappings in partial b-metric spaces and application, Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019),
no. 2, 97–108.
[4] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Func. An. Gos. Ped. Inst. Unianowsk 30
(1989), 26–3[5] A. Branciari, A fixed point theorem of banach-caccioppoli type on a class of generalized metric spaces, Pub. Math.
Debercen 57 (2000), 31–37.
[6] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int.
J. Math. Math. Sci. 29 (2002), no. 9, 531–536.
[7] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostraviensis 1 (1993), no. 1, 5–11.
[8] R. George, S. Radenovic, K.P. Reshma and S. Shukla, Rectangular b-metric space and contraction principles, J.
Nonlinear Sci. Appl. 8 (2015), no. 6, 1005–1013.
[9] R. Jain, H. Kumar Nashine, R. George and Z.D. Mitrovi´c, On extended branciari-distance spaces and applications
to fractional differential equations, J. Funct. Spaces 2021 (2021).
[10] T. Kamran, M. Samreen and Q.U. Ain, A generalization of b-metric space and some fixed point theorems, Math.
5 (2017), no. 2, 19.
[11] E. Karapinar, P. Kumam and P. Salimi, On α-ψ-meir-keeler contractive mappings, Fixed Point Theory Appl.
2013 (2013), no. 1, 1–12.
[12] A. Latif, J. Rezaei Roshan, V. Parvaneh and N. Hussain, Fixed point results via α-admissible mappings and cyclic
contractive mappings in partial b-metric spaces, J. Inequal. Appl. 2014 (2014), no. 1, 1–26.
[13] N.T.T. Ly and N.T. Hieu, Some fixed point theorems for genaralized α-β-fg-contractions in b-metric spaces and
certain applications to the integral equations, East West Math. 20 (2018), no. 1, 86–106.
[14] N. Mlaiki, M. Hajji and T. Abdeljawad, A new extension of the rectangular-metric spaces, Adv. Math. Phys.
2020 (2020).
[15] H. Kumar Nashine, Z. Kadelburg and R.P. Agarwal, Existence of solutions of integral and fractional differential
equations using α-type rational f-contractions in metric-like spaces, Kyungpook Math. J. 58 (2018), no. 4, 651–
[16] V. Parvaneh, N. Hussain and Z. Kadelburg, Generalized wardowski type fixed point theorems via α-admissible
fg-contractions in b-metric spaces, Acta Math. Sci. 36 (2016), no. 5, 1445–1456.
[17] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α–ψ-contractive type mappings, Nonlinear Anal. 75
(2012), no. 2, 2154–2165.
[18] D. Wardowski and N. Van Dung, Fixed points of f-weak contractions on complete metric spaces, Demonstr. Math.
47 (2014), no. 1, 146–155.
[19] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory
Appl. 2012 (2012), no. 1, 1–6.
Volume 13, Special Issue for selected papers of ICDACT-2021
The link to the conference website is
March 2022
Pages 17-29
  • Receive Date: 15 August 2021
  • Revise Date: 18 December 2021
  • Accept Date: 01 January 2022