AIMS Mathematics, 2020, 5(5): 4853-4873. doi: 10.3934/math.2020310.

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

(F, h)-upper class type functions for cyclic admissible contractions in metric spaces

1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2 School of Mathematics, Thapar University, Patiala-147004, India
3 Department of Pharmaceutical Sciences, Vasile Goldiş Western University of Arad, Liviu Rebreanu Street, no. 86, 310414 Arad, Romania
4 Computer Engineering Department, Komar University of Science and Technology, Sulaymaniyah 46001, Kurdistan Region, Iraq
5 Department of Mathematics, University of Seoul, Seoul 02504, Korea
6 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

In this paper, we introduce the notions of T-cyclic (α, β, H, F)-contractive mappings using a pair (F, h)-upper class functions type in order to obtain new common fixed point results in the settings of metric spaces. The presented results generalize and extend existing results in the literature.
  Figure/Table
  Supplementary
  Article Metrics

Keywords common fixed point; point of coincidence; T-cyclic (α, β)-admissible mapping; T-cyclic (α, β, H, F)-contractive mappings; pair (F, h)-upper class

Citation: Arslan Hojat Ansari, Sumit Chandok, Liliana Guran, Shahrokh Farhadabadi, Dong Yun Shin, Choonkil Park. (F, h)-upper class type functions for cyclic admissible contractions in metric spaces. AIMS Mathematics, 2020, 5(5): 4853-4873. doi: 10.3934/math.2020310

References

  • 1. Ö, Acar, A fixed point theorem for multivalued almost F-δ-contraction, Results Math., 72 (2017), 1545-1553.    
  • 2. S. Alizadeh, F. Moradlou and P. Salimi, Some fixed point results for (α, β)-(ψ, φ)-contractive mappings, Filomat, 28 (2014), 635-647.    
  • 3. A. H. Ansari and S. Shukla, Some fixed point theorems for ordered F-(\mathcal{F}, h)-contraction and subcontractions in 0- f -orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), 37-53.
  • 4. A. H. Ansari, P. Vetro and S. Radenović, Integration of type pair (H, F) upclass in fixed point result for GP(Γ,Θ)-contractive mappings, Filomat, 31 (2017), 2211-2218.
  • 5. H. Aydi, M. Abbas and C. Vetro, Common fixed points for multivalued generalized contractions on partial metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 108 (2014), 483-501.
  • 6. G. V. R. Babu and P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math., 9 (2011), 1-10.
  • 7. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181.    
  • 8. T. C. Bhakta and S. Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl., 98 (1984), 348-362.    
  • 9. 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.
  • 10. S. H. Cho and J. S. Bae, Fixed points of weak α-contraction type maps, Fixed Point Theory Appl., 2014 (2014), 175.
  • 11. D. Gopal, M. Abbas and C. Vetro, Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation, Appl. Math. Comput., 232 (2014), 955-967.
  • 12. M. Imdad, S. Chauhan, Z. Kadelburg, et al. Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dynamic programming, Appl. Math. Comput., 227 (2014), 469-479.
  • 13. H. Isik, B. Samet and C. Vetro, Cyclic admissible contraction and applications to functional equations in dynamic programming, Fixed Point Theory Appl., 2015 (2015), 163.
  • 14. G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238.
  • 15. Z. Kadelburg and S. Radenovic, On generalized metric spaces: a survey, TWMS J. Pure Appl. Math., 5 (2014), 3-13.
  • 16. M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9.    
  • 17. W. A. Kirk, P. S. Srinavasan and P. Veeramani, Fixed points for mapping satisfying cylical contractive conditions, Fixed Point Theory, 4 (2003), 79-89.
  • 18. S. Kumar, A short survey of the development of fixed point theory, Surveys Math. Appl., 8 (2013), 91-101.
  • 19. M. Pacurar and I. A. Rus, Fixed point theory for cyclic φ-contractions, Nonlinear Anal., 72 (2010), 1181-1187.    
  • 20. A. Padcharoen, D. Gopal, P. Chaipunya, et al. Fixed point and periodic point results for α-type F-contractions in modular metric spaces, Fixed Point Theory Appl., 2016 (2016), 39.
  • 21. S. Radenović and S. Chandok, Simulation type functions and coincidence points, Filomat, 32 (2018), 141-147.    
  • 22. B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683-2693.    
  • 23. S. Romaguera and P. Tirado, Characterizing complete fuzzy metric spaces via fixed point results, Mathematics, 8 (2020), 273.
  • 24. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.    
  • 25. Z. Wu, A fixed point theorem, intermediate value theorem and nested interval property, Anal. Math., 45 (2019), 443-447.
  • 26. C. Zhua, W. Xua, T. Došenović, et al. Common fixed point theorems for cyclic contractive mappings in partial cone b-metric spaces and applications to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 807-827.    

 

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved