Fixed Point Results of Rational Type-contraction Mapping in b-Metric Spaces with an Application

  • Mashkhas M. Hussein Department of Mathematics, College of Education, Aden University, Aden, Yemen
  • Maged G. Bin-Saad Department of Mathematics, College of Education, Aden University, Aden, Yemen
  • Anter A. Al-Sayad Department of Mathematics, College of Education, Aden University, Aden, Yemen
Keywords: fixed point, b-metric space, rational contraction mapping, nonlinear integral equation

Abstract

In this article, we establish the existence of fixed points of rational type contractions in the setting of b-metric spaces and we verify the T-stability of the P property for some mappings. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.

References

B. Alqahtani, A. Fulga, E. Karapınar and V. Rakočević, Contractions with rational inequalities in the extended b-metric space, Journal of Inequalities and Applications 2019 (2019), Article No. 220. https://doi.org/10.1186/s13660-019-2176-6

A. Amini-Harandi, Fixed point theorem for quasi-contraction mopa in b-metric spaces, Fixed Point Theory 15(2) (2014), 351-358.

I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations integrals, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181

M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metric, Stud. Univ. Babeş-Bolyai Math. 54 (2009), 3-14.

I. Cabrera, J. Harjani and K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat. 59(2) (2013), 251-258. https://doi.org/10.1007/s11565-013-0176-x

S. Chatterjee, Fixed point theorems, Dokladi na Bolgarskata Akademiya na Naukite 25(6) (1972), 727-730.

B. S. Choudhury, N. Metiya and P. Konar, Fixed point results for rational type contraction in partially ordered complex valued metric spaces, Bull. Int. Math. Virtual Inst. 5(1) (2015), 73-80. https://doi.org/10.18576/msl/050207

S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1(1) (1993), 5-11.

B. K. Dass and S. Gupta, An extension of banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6(12) (1975), 1455-1458.

B. Fisher, A fixed point theorem for compact metric spaces, Publ. Math. Debrecen 25 (1978), 193-194. https://doi.org/10.5486/pmd.1978.25.3-4.01

B. Fisher, A note on a theorem of Khan, J. Math. 10 (1978).

H. Huang, G. Deng and S. Radenović, Fixed point theorems in b-metric spaces with applications to differential equations, J. Fixed Point Theory Appl. 20(1) (2018), Paper No. 52, 24 pp. https://doi.org/10.1007/s11784-018-0491-z

D. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8(2) (1977), 223-230.

G. Jeong and B. Rhoades, Maps for which F(T) = F(T^n), Fixed Point Theory Appl. 6 (2005), 87-131.

T. Kamran, M. Samreen and Q. UL Ain, A generalization of b-metric space and some fixed point theorems, Mathematics 5(2) (2017), 19. https://doi.org/10.3390/math5020019

R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc. 60 (1968), 71-76.

M. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Analysis: Theory, Methods & Applications 73(9) (2010), 3123-3129. https://doi.org/10.1016/j.na.2010.06.084

M. Khan, A fixed point theorem for metric spaces, J. Math. 8 (1976).

K. Mohammad and P. Jhade, On a fixed point theorem with PPF dependence in the Razumikhin class, Gazi University Journal of Science 28(2) (2015), 211-219.

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 7(1) (2015), 70-78.

W. Sintunavarat, Nonlinear integral equations with new admissibility types in b-metric spaces, Journal of Fixed Point Theory and Applications 18(2) (2016), 397-416. https://doi.org/10.1007/s11784-015-0276-6

S. Xie, Y. Wang and L. Zhong, Some fixed point theorems in b-metric spaces, International Journal of Pure and Applied Mathematics 110(4) (2016), 571-580. https://doi.org/10.12732/ijpam.v110i4.1

Published
2023-03-23
How to Cite
Hussein, M. M., Bin-Saad, M. G., & Al-Sayad, A. A. (2023). Fixed Point Results of Rational Type-contraction Mapping in b-Metric Spaces with an Application. Earthline Journal of Mathematical Sciences, 12(2), 141-164. https://doi.org/10.34198/ejms.12223.141164
Section
Articles