Some Common Fixed Point Theorems of Rational Contractions Condition in Generalized Banach Space


  • Wesam N. Khuen Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, IRAQ.
  • Alia S. Hassan Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah, IRAQ.



fixed points, common fixed point, Banach space, Cauchy sequence, rational contractions condition.


In this work, we introduce some common fixed points theorems type rational contractions on generalized Banach space. The provided theorem is a generalization and an extension of many well-known theorems; we present a few examples to illustrate the validity of the results obtained in the paper.


Bakhtin, I. (1989). The contraction mapping principle in quasimetric spaces. Functional analysis, 30, 26-37.‏

Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. math, 3(1), 133-181.‏

CrossRef DOI:

‏[3] Czerwik, S. (1993). Contraction mappings in $ b $-metric spaces. Acta mathematica et informatica universitatis ostraviensis, 1(1), 5-11.

Boriceanu, M. (2009). fixed point theory for multivalued generalized contraction on a set with two b-metrics. studia Universitatis Babes-Bolyai, Mathematica, (3).‏

Bota, M., Molnar, A., & Varga, C. S. A. B. A. (2011). On Ekeland's variational principle in b-metric spaces. Fixed Point Theory, 12(2), 21-28.‏‏

Ding, H. S., Imdad, M., Radenović, S., & Vujaković, J. (2016). On some fixed point results in b-metric, rectangular and b-rectangular metric spaces. Arab Journal of Mathematical Sciences, 22(2), 151-164.‏

CrossRef DOI:

Kir, M., & Kiziltunc, H. (2013). On some well known fixed point theorems in b-metric spaces. Turkish journal of analysis and number theory, 1(1), 13-16.‏

CrossRef DOI:

Mohammad, K, & Pankaj J. (2015). On A Fixed Point Theorem with PPF Dependance in the Razumikhin Class. Gazi University Journal of Science, 28(2), 211-219.‏

Ozturk, V., & Turkoglu, D. (2015). Common fixed point theorems for mappings satisfying (EA)-property in b-metric spaces. J. Nonlinear Sci. Appl, 8(6), 1127-1133.‏

CrossRef DOI:

Sarwar, M., & Rahman, M. U. (2015). Fixed Point Theorems for Ciric's and Generalized Contractions in b-metric spaces. International journal of analysis and applications, 7(1), 70-78.‏

Seddik, M., & Taieb, H. (2021). Some fixed point theorems of rational type contraction in-metric spaces. Moroccan Journal of Pure and Applied Analysis, 7(3), 350-363.‏

CrossRef DOI:

Xie, S., Wang, Y., & Zhong, L. (2016). SOME FIXED POINT THEOREMS IN $ b $-METRIC SPACES. International Journal of Pure and Applied Mathematics, 110(4), 571-580.‏

CrossRef DOI:

Bhardwaj, R., Wadkar, B. R., & Singh, B. (2015). Fixed point theorems in generalized Banach Space. International journal of Computer and Mathematical Sciences (IJCMS), ISSN, 2347-8527.




How to Cite

W. N. . Khuen and A. S. . Hassan, “Some Common Fixed Point Theorems of Rational Contractions Condition in Generalized Banach Space”, Al-Mustansiriyah Journal of Science, vol. 33, no. 3, pp. 60–65, Sep. 2022.