Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

RESULTS IN b-METRIC SPACES ENDOWED WITH THE GRAPH AND APPLICATION TO DIFFERENTIAL EQUATIONS

  • SATYENDRA KUMAR JAIN (Department of Mathematics, St. Aloysius College Jabalpur) ;
  • GOPAL MEENA (Department of Applied Mathematics, Jabalpur Engineering College) ;
  • LAXMI RATHOUR (Department of Mathematics, Indira Gandhi National Tribal University) ;
  • LAKSHMI NARAYAN MISHRA (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology)
  • Received : 2023.04.11
  • Accepted : 2023.06.07
  • Published : 2023.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this research, under some specific situations, we precisely derive new coupled fixed point theorems in a complete b-metric space endowed with the graph. We also use the concept of coupled fixed points to ensure the solution of differential equations for the system of impulse effects.

Keywords

References

  1. S. Aleksic, Z.D. Mitrovic, S. Redanovic, Picard sequence in 𝑏-metric spaces, Fixed Point Theory 21 (2020), 35-46.  https://doi.org/10.24193/fpt-ro.2020.1.03
  2. A.H. Ansari Komachali, Ya'e Ulrich Gaba, Maggie Aphane, Isa Yildirim , Refinement on fixed point results in metric and 𝑏-metric spaces, Filomat 37:22 (2023), 7581-7588. 
  3. R. Arab, K. Zare, Fixed point results for rational type contractions in partially ordered 𝑏-metric spaces, International Journal of Analysis and Applications 2291-8639 10 (2016), 64-70. 
  4. M.R. Alfuraidan and M.A. Khamsi, Coupled fixed points of monotone mappings in a metric space with a graph, arXiv 2018. 
  5. I. Beg, A. Butt, S. Radojevic, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl. 60 (2010), 1214-1219.  https://doi.org/10.1016/j.camwa.2010.06.003
  6. T.G. Bhaskar and V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods and Applications 65 (2006), 1379-1393.  https://doi.org/10.1016/j.na.2005.10.017
  7. F. Bojor, Fixed point of ϕ-contraction in metric spaces endowed with a graph, Ann. Univ. Craiova Math. Comput. Sci. Ser. 37 (2010), 85-92. 
  8. F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal. Theory Methods Appl. 75 (2012), 3895-3901.  https://doi.org/10.1016/j.na.2012.02.009
  9. F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, Analele Univ. Ovidius Constanta-Ser. Mat. 20 (2012), 31-40. 
  10. N. Boonsri and S. Saejung, Fixed point theorems for contractions of Reich type on a metric space with a graph, J. Fixed Point Theory Appl. 20 (2018), 84. 
  11. S. Chandok, T.D. Narang and M.A. Taoudi Some coupled fixed point theorems for mappings satisfying a generalized contractive condition of rational type, Palestine Journal of Mathematics 4 (2015), 360-366 
  12. H. Huang, S. Radenovic, G. Deng, A sharp generalization on cone 𝑏-metric space over Banach algebra, J. Nonlinear Sci. Appl. 10 (2017), 429-435.  https://doi.org/10.22436/jnsa.010.02.09
  13. J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Am. Math. Soc. 136 (2008), 1359-1373.  https://doi.org/10.1090/S0002-9939-07-09110-1
  14. G. Mani, L.N. Mishra and V.N. Mishra, Common fixed point theorems in complex partial 𝑏-metric space with an application to integral equations, Adv. Studies: Euro-Tbilisi Math. J. 15 (2022), 129-149. 
  15. L.N. Mishra, V. Dewangan, V.N. Mishra, H. Amrulloh, Coupled best proximity point theorems for mixed g-monotone mappings in partially ordered metric spaces, J. Math. Comput. Sci. 11 (2021), 6168-6192. 
  16. A.G. Sanatee, L. Rathour, V.N. Mishra, V. Dewangan, Some fixed point theorems in regular modular metric spaces and application to Caratheodory's type anti-periodic boundary value problem, The Journal of Analysis 31 (2023), 619-632. 
  17. P. Shahi, L. Rathour, V.N. Mishra, Expansive Fixed Point Theorems for tri-simulation functions, The Journal of Engineering and Exact Sciences-jCEC 08 (2022), 14303-01e. 
  18. N. Sharma, L.N. Mishra, V.N. Mishra, S. Pandey, Solution of Delay Differential equation via Nv1 iteration algorithm, European J. Pure Appl. Math. 13 (2020), 1110-1130. https://doi.org/10.29020/nybg.ejpam.v13i5.3756