Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
권호 표지
DOI QR코드

DOI QR Code

𝜓-COUPLED FIXED POINT THEOREM VIA SIMULATION FUNCTIONS IN COMPLETE PARTIALLY ORDERED METRIC SPACE AND ITS APPLICATIONS

  • Das, Anupam (Department of Mathematics, Cotton University, Department of Mathematics, Rajiv Gandhi University) ;
  • Hazarika, Bipan (Department of Mathematics, Guwahati University) ;
  • Nashine, Hemant Kumar (Applied Analysis Research Group, Faculty of Mathematics and Statistics Ton Duc Thang University) ;
  • Kim, Jong Kyu (Department of Mathematics Education, Kyungnam University)
  • Received : 2020.08.20
  • Accepted : 2020.10.06
  • Published : 2021.06.15
Download PDF
⟨ Previous Next ⟩

Abstract

We proposed to give some new 𝜓-coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.

Keywords

Acknowledgement

This work was supported by the Basic Science Research Program through the National Research Foundation(NRF) Grant funded by Ministry of Education of the republic of Korea (2018R1D1A1B07045427).

References

  1. M. Abbas, M.A. Khan and S. Radenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202. https://doi.org/10.1016/j.amc.2010.05.042
  2. H. Aydi, E. Karapinar and B. Samet, Remarks on some recent fixed point theorems, Fixed Point Theory Appl., 2012 (76) (2012).
  3. A. Amini Harandi, Coupled and tripled fixed point theory in partially ordered metric spaces with applications to initial value problem, Math. Comput. Model., 57 (2011), 2343-2348, http://dx.doi.org/10.1016/ j.mcm.2011.12.006.
  4. A. Bataihah, W. Shatanawi and A. Tallafha, Fixed point results with simulation functions, Nonlinear Funct. Anal. Appl., 25(1) (2020), 13-23, doi.org/10.22771/nfaa.2020.25.01.02.
  5. V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal.: TMA, 74 (2011), 7347-7355. https://doi.org/10.1016/j.na.2011.07.053
  6. T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.: TMA, 65(7) (2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
  7. M. Borcut, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218 (2012), 7339-7346. https://doi.org/10.1016/j.amc.2012.01.030
  8. D. Doric, Z. Kadelburg, S. Radenovic and P. Kumam, A note on fixed point results without monotone property in partially ordered metric spaces, RACSAM., 108 (2014), 503-510. https://doi.org/10.1007/s13398-013-0121-y
  9. Y. Fan, C. Zhu and Z. Wu, Some φ-coupled fixed point results via modified F-control function's concept in metric spaces and its applications, J. Comput. Appl. Math., 349 (2019), 70-81. https://doi.org/10.1016/j.cam.2018.09.013
  10. D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal.: TMA, 11 (1987), 623-632. https://doi.org/10.1016/0362-546X(87)90077-0
  11. B. Hazarika, H.M. Srivastava, R. Arab and M. Rabbani, Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution, Appl. Math. Comput., 360 (2019), 131-146.
  12. B. Hazarika, R. Arab and P. Kumam, Coupled fixed point theorems in partially ordered metric spaces via mixed g-monotone property, J. Fixed Point Theory Appl., 29(1) (2019), 1-19.
  13. Ding Hui-Sheng, L. Li and S. Radenovic, Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces, Fixed Point Theory Appl., 2012(96) (2012).
  14. J. Jachymski, Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 194 (1995), 293-303. https://doi.org/10.1006/jmaa.1995.1299
  15. M. Jleli, B. Samet and C. Vetro, Fixed point theory in partial metric spaces via φ-fixed point's concept in metric spaces, J. Inequal. Appl., 2014(426) (2014).
  16. A. Karami, S. Sedghi, N. Shobe and H.G. Hyun, Fixed point results on s-metric space via simulation functions , Nonlinear Funct. Anal. Appl., 24(4) (2019), 665-674, doi.org/10.22771/nfaa.2019.24.04.02
  17. S. Matthews, Partial metric topology, Ann. New York Acad. Sci, (1994), 183-197.
  18. H. K. Nashine and I. Altun, New fixed point results for maps satisfying implicit relations on ordered metric spaces and application, Appl. Math. Comput., 240 (2014), 259-272. https://doi.org/10.1016/j.amc.2014.04.073
  19. V. I. Opoitsev, Heterogenic and combined-concave operators, Syber. Math. J., 16 (1975), 781-792 (in Russian).
  20. V. I. Opoitsev, Dynamics of collective behavior. III. Heterogenic system, Avtomat. i Telemekh., 36 (1975), 124-138 (in Russian).
  21. A. Padcharoen and J.K. Kim, Berinde type resukts via simulation functions in metric spaces, Nonlinear Funct. Anal. Appl., 25(3) (2020), 665-674, doi.org/10.22771/nfaa.2020.25.03.07.
  22. S. Radenovic, Remarks on some coupled coincidence point results in partially ordered metric spaces, Arab J Math Sci., 20(1) (2014), 29-39. https://doi.org/10.1016/j.ajmsc.2013.02.003
  23. S. Radenovic, Some coupled coincidence points results of monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5(2) (2014), 174-184.
  24. S. Radenovic, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujev. J. Math., 38(2) (2014), 249-257. https://doi.org/10.5937/KgJMath1402249R
  25. A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443. https://doi.org/10.1090/S0002-9939-03-07220-4
  26. A. Razani and V. Parvaneh, Coupled coincidence point results for (ψ, α, β)-weak contractions in partially ordered metric spaces, J. Appl. Math., 2012 (2012). Article ID 496103.