Nonlinear Functional Analysis and Applications

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

DOI QR Code

SOME FIXED POINT THEOREMS FOR RATIONAL (𝛼, 𝛽, Z)-CONTRACTION MAPPINGS UNDER SIMULATION FUNCTIONS AND CYCLIC (𝛼, 𝛽)-ADMISSIBILITY

  • Snehlata, Mishra (Dr. C. V. Raman University) ;
  • Anil Kumar, Dubey (Department of Mathematics, Bhilai Institute of Technology) ;
  • Urmila, Mishra (Department of Mathematics, Vishwavidyalaya Engineering College (A Constituent College of CSVTU)) ;
  • Ho Geun, Hyun (Department of Mathematics Education, Kyungnam University)
  • Received : 2021.11.20
  • Accepted : 2022.06.21
  • Published : 2022.12.06
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we present some fixed point theorems for rational type contractive conditions in the setting of a complete metric space via a cyclic (𝛼, 𝛽)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.

Keywords

Acknowledgement

The authors are thankful to the learned referee for his/her deep observations and their suggestions, which greatly helped us to improve the paper significantly.

References

  1. S. Alizadeh, F. Moradlou and P. Salimi, Some fixed point results for (α, β)-(ψ, φ)-contractive mappings, Filomat, 28(3) (2014), 635-647. https://doi.org/10.2298/FIL1403635A
  2. H.H. Alsulami, E. Karapinar, F. Khojasteh and A.F. Roldan-Lopez-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dyna. Nature and Soc., (2014) Article ID 269286, 1-10.
  3. A.H. Ansari, J. Nantadilok and M.S. Khan, Best proximity points of generalized cyclic weak (F, ψ, ϕ)-contractions in ordered metric spaces, Nonlinear Funct. Anal. Appl., 25(1) (2020), 55-67.
  4. H. Argoubi, B. Samet and C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (2015), 1082-1094. https://doi.org/10.22436/jnsa.008.06.18
  5. H. Aydi and A. Felhi, Fixed points in modular spaces via α-admissible mappings and simulation functions, J. Nonlinear Sci. Appl., 9 (2016), 3686-3701. https://doi.org/10.22436/jnsa.009.06.20
  6. H. Aydi, A. Felhi and S. Sahmim, On common fixed points for (α, ψ)-contractions and generalized cyclic contractions in b-metric like spaces and consequences, J. Nonlinear Sci. Appl., 9 (2016), 2492-2510. https://doi.org/10.22436/jnsa.009.05.48
  7. H. Aydi, E. Karapinar and V. Rakocevic, Non unique fixed point theorem on b-metric spaces via simulation functions, Jordan J. Math. Stat., 12 (2019), 265-288.
  8. M. Bousselsal and Z. Mostefaoui, Some common fixed point results in partial metric spaces for generalized rational type contraction mappings, Nonlinear Funct. Anal. Appl., 20(1) (2015), 43-54.
  9. Seong-Hoon Cho, Fixed point theorem for (α, β)-z contractions in metric spaces, Int. J. Math. Anal., 13(4) (2019), 161-174. https://doi.org/10.12988/ijma.2019.9318
  10. A. Das, B. Hazarika, H.K. Nashine and J.K. Kim, ψ-coupled fixed point theorem via simulation functions in complete partially ordered metric space and its applications, Nonlinear Funct. Anal. Appl., 26(2) (2021), 273-288. https://doi.org/10.22771/NFAA.2021.26.02.03
  11. E. Karapinar Fixed points results via simulation functions, Filomat, 30 (2016), 2343-2350. https://doi.org/10.2298/FIL1608343K
  12. E. Karapinar and F. Khojasteh, An approach to best proximity point results via simulation functions, J. Fixed Point Theorey Appl., 19 (2017), 1983-1995. https://doi.org/10.1007/s11784-016-0380-2
  13. E. Karapinar and B. Samet, Generalized α - ψ contractive type mappings and related fixed point theorems with applications, Abst. Appl. Anal., 2012 (2012), 17 pages.
  14. F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theory for simulation function, Filomat, 29(6) (2015), 1189-1194. https://doi.org/10.2298/FIL1506189K
  15. H.K. Nashine, R.W. Ibrahim, Y.J. Cho and J.K. Kim, Fixed point theorems for the modified simulation function and applications to fractional economics systems, Nonlinear Funct. Anal. Appl., 26 (1) (2021), 137-155. https://doi.org/10.22771/NFAA.2021.26.01.10
  16. H. Qawagneh, M.S. Noorani, W. Shatanawi, K. Abodayeh and H. Alsamir, Fixed point for mappings under contractive condition based on simulation functions and cyclic (α, β)-admissibility, J. Math. Anal., 9(1) (2018), 38-51.
  17. A.F. Roldan-Lopez-de-Hierro, E. Karapinar, C. Roldan-Lopez-de-Hierro and J. Martinez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), 345-355. https://doi.org/10.1016/j.cam.2014.07.011
  18. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for (α - ψ)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014