A general common fixed point result for two pairs of maps in b-metric spaces


  • Mohamed Akkouchi University Cadi Ayyad.




Complete b-metric spaces, Implicit relations, Common fixed point for four maps, Weakly compatible maps, Compatible maps


We establish a general common fixed point problem for two pairs {f, S} and {g, T } of weakly compatibles selfmaps of a complete b-metric (X, d; s). These maps are satisfying a contractive condition defined by a class of implicit relations in five variables. This contraction unifies, in one go, several contractive conditions previously used in a set of recent papers dealing with fixed point or common fixed results for selfmaps of b-metric spaces. We provide an illustrative example.

Author Biography

Mohamed Akkouchi, University Cadi Ayyad.

Dept. of Mathematics, Faculty of Sciences-Semlalia.


M. Akkouchi, “A common fixed point theorem connected to a result of V. Popa and H. K. Pathak”, Georgian mathematical journal, vol. 13, no. 1, pp. 1–6, 2006, doi: 10.1515/GMJ.2006.1

M. Akkouchi, “Common fixed point theorems for two selfmappings of a b-metric space under an implicit relation”, Hacettepe journal of mathematics and statistics, vol. 40, no. 6, pp. 805-810, 2011. [On line]. Available: https://bit.ly/3cmWXg4

M. Akkouchi, “A common fixed point theorem for expansive mappings under strict implicit conditions on b-metric spaces”, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 50, no. 1, pp. 5-15, 2011. [On line]. Available: https://bit.ly/3ckvvjf

M. Akkouchi, “A common fixed point theorem for two pairs of weakly tangential maps in b-metric spaces”, Journal of the International Mathematical Virtual Institute, vol. 9, pp. 189-204, 2019. [On line]. Available: https://bit.ly/2FXthKn

I. A. Bakhtin, “The contraction mapping principle in quasimetric spaces”, Functional analysis, vol. 30, pp. 26-37, 1989.

V. Berinde, “Generalized contractions in quasimetric spaces,” in Seminar on fixed point theory, vol. 3, Cluj-Napoca: "Babeg-Bolyai" University, Faculty of Mathematics and Computer Science, 1993, pp. 3–9. [On line]. Available: https://bit.ly/2ZX4uNS

S. Cobza?, “B-metric spaces, fixed points and Lipschitz functions, Apr. 2018. arXiv:1802.02722v2

S. Czerwik, “Contraction mappings in b-metric spaces”, Acta mathematica et informatica Universitatis Ostraviensis, vol. 1, no. 1, pp. 5-11, 1993. [On line]. Available: https://bit.ly/3hT7LUt

S. Czerwik, “Nonlinear set-valued contraction mappings in B-metric spaces”, Atti del seminario matematico e fisico dell'Universita di Modena e Reggio Emilia, vol. 46, no. 2, pp. 263- 276, 1998.

T. Dosenovi?, M. Pavlovi?, and S. Radenovi?, “Contractive conditions in b-metric spaces”, Vojnotehnicki glasnik, vol. 65, no. 4, pp. 851–865, 2017, doi: 10.5937/vojtehg65-14817

N. Hussain, Z. D. Mitrovi?, and S. Radenovi?, “A common fixed point theorem of Fisher in b-metric spaces”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 113, no. 2, pp. 949–956, 2018, doi: 10.1007/s13398-018-0524-x

M. Jovanovi?, Z. Kadelburg, and S. Radenovi?, “Common fixed point results in metric-type spaces”, Fixed point theory and applications, vol. 2010, no. 1, Art ID. 978121, 2010, doi: 10.1155/2010/978121

G. Jungck, “Compatible mappings and common fixed points”, International journal of mathematics and mathematical sciences, vol. 9, no. 4, pp. 771–779, 1986, doi: 10.1155/S0161171286000935

G. Jungck, “Common fixed points for noncontinuous nonself maps on nonmetric spaces”, Far eastern journal of mathematics and science, vol. 4, no. 2, pp. 199-215, 1996.

W. Kirk and N. Shahzad, Fixed point theory in distance spaces. Cham: Springer International Publishing, 2014, doi: 10.1007/978-3-319-10927-5

R. Miculescu and A. Mihail, “Caristi-Kirk type and Boyd and Wong-Browder-Matkowski-Rus type fixed point results in b-metric spaces”, Filomat, vol. 31, no. 14, pp. 4331-4340, 2017, doi: 10.2298/FIL1714331M

P. K. Mishra, S. Sachdeva, and S. K. Banerjee, “Some fixed point theorems in b-metric space”, Turkish journal of analysis and number theory, vol. 2, no. 1, pp. 19-22, 2014, doi: 10.12691/tjant-2-1-5

M. Paluszy?ski and K. Stempak, “On quasi-metric and metric spaces”, Proceeding American Mathematical Society, vol. 137, no. 12, pp. 4307-4312, Dec. 2009, doi: 10.1090/S0002-9939-09-10058-8

M. Sarwar and M.U. Rahman, “Fixed point theorems for Ciric’s and generalized contractions in b-metric spaces”, International journal of analysis and applications, vol. 7, no. 1, pp. 70-78, 2015. [On line]. Available: https://bit.ly/3hQBmOp

T. Suzuki, “Basic inequality on a b-metric space and its applications”, Journal of inequalities and applications, vol. 2017, Art ID. 256, Oct. 2017, doi: 10.1186/s13660-017-1528-3



How to Cite

M. Akkouchi, “A general common fixed point result for two pairs of maps in b-metric spaces”, Proyecciones (Antofagasta, On line), vol. 39, no. 5, pp. 1251-1266, Oct. 2020.