Some Results of Rational Contraction Mapping via Extended CF-Simulation Function in Metric-Like Space with Application

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Habes Alsamir, Some Results of Rational Contraction Mapping via Extended CF-Simulation Function in Metric-Like Space with Application, Int. J. Anal. Appl., 19 (1) (2021), 138-152.

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Habes Alsamir

Abstract

In this paper, we introduce a new contraction via CF -simulation function and prove the existence and the uniqueness of our mapping defined on a metric-like space. Our work generalizes and extends some theorems in the literature. An example and application of second type of Fredholm integral equation are given.

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References

  1. S. Banach, Sur les Operations dans les Ensembles Abstraits et Leur Applications aux Equations Integrals, Fund. Math. 3 (1922), 133-181.
  2. H. Qawaqneh, M. Noorani, W. Shatanawi, H. Alsamir, Common Fixed Point Theorems for Generalized Geraghty (α, ψ, φ)- Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces, Axioms. 7 (2018), 74.
  3. H. Alsamir, M. Selmi Noorani, W. Shatanawi, H. Aydi, H. Akhadkulov, H. Qawaqneh, K. Alanazi, Fixed Point Results in Metric-like Spaces via Sigma-simulation Functions, Eur. J. Pure Appl. Math. 12 (2019), 88-100.
  4. A.F. Roldan-L ´opez-de-Hierro, E. Karapinar, C. Rold ´an-L ´opez-de-Hierro, J. Mart ´iinez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 275 (2015), 345-355.
  5. X.L. Liu, A.H. Ansari, S. Chandok, S. Radenovic, On some results in metric spaces using auxiliary simulation functions via new functions, J. Comput. Anal. Appl. 24(6) (2018), 1103-1114.
  6. H. Aydi, A. Felhi, Best proximity points for cyclic Kannan-Chatterjea- Ciric type contractions on metric-like spaces, J. Nonlinear Sci. Appl. 9 (2016), 2458-2466.
  7. H. Aydi, A. Felhi, On best proximity points for various alpha-proximal contractions on metric-like spaces, J. Nonlinear Sci. Appl. 9 (2016), 5202-5218.
  8. H. Alsamir, M.S. Md Noorani H. Qawagneh, K. Alanazi, Modified cyclic(α, β)-admissible Z-contraction mappings in metric-like spaces, Asia-Pacific Conference on Applied Mathematics and Statistics, 2019.
  9. H. Alsamir, M. Noorani, W. Shatanawi, K. Abodyah, Common fixed point results for generalized (ψ, β)-Geraghty contraction type mapping in partially ordered metric-like spaces with application, Filomat 31(17) (2017), 5497-5509.
  10. H. Aydi, A. Felhi, H. Afshari, New Geraghty type contractions on metric-like spaces, J. Nonlinear Sci. Appl. 10 (2017), 780-788.
  11. A.A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012 (2012), 204.
  12. E. Karapinar, P. Salimi, Dislocated metric space to metric spaces with some fixed point theorems, Fixed Point Theory Appl. 2013 (2013), 222.
  13. F.Yan, Y. Su, Q. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory Appl. 2012 (2012), 152.
  14. B. Samet, C. Vetro, P. Vetro, Fixed point theorems for a α - ψ-contractive type mappings. Nonlinear Anal., Theory Meth. Appl. 75(4) (2012), 2154-2165.
  15. H. Alsamir, M. Noorani,W. Shatanawi, F. Shaddad, Generalized Berinde-type (η, ξ, Ï‘, θ) contractive mappings in b-metric spaces with an application, J. Math. Anal. 7(6) (2016), 1-12.
  16. H. Alsamir, M. Noorani, W. Shatanawi, On fixed points of (η, θ)-quasi contraction mappings in generalized metric spaces. J. Nonlinear Sci. Appl. 9 (2016), 4651-4658.
  17. H. Alsamir, M. S. M. Noorani, W. Shatanawi, On new fixed point theorems for three types of (α, β) - (ψ, θ, φ)-multivalued contractive mappings in metric spaces. Cogent Math. 3(1) (2016), 1257473.
  18. W. Shatanawi, M. Noorani, J. Ahmad, H. Alsamir, M. Kutbi, Some common fixed points of multivalued mappings on complex-valued metric spaces with homotopy result. J. Nonlinear Sci. Appl. 10 (2017), 3381-3396.
  19. H. Akhadkulov, M. S. Noorani, A. B. Saaban, F. M. Alipiah, H. Alsamir. Notes on multidimensional fixed-point theorems. Demonstr. Math. 50(1) (2017), 360-374.
  20. H. Qawagneh, Noorani, W. Shatanawi, H. Alsamir. Common fixed points for pairs of triangular α-admissible mappings. J. Nonlinear Sci. Appl 10 (2017), 6192-6204.
  21. H. Qawagneh, M. S. M. Noorani, W. Shatanawi, K. Abodayeh, H. Alsamir. Fixed point for mappings under contractive condition based on simulation functions and cyclic (α, β)-admissibility. J. Math. Anal. 9 (2018), 38-51.
  22. H. Alsamir, M. Noorani, W. Shatanawi, Fixed point results for new contraction involving C-class functions in partial metric spaces, https://www.researchgate.net/publication/332396635_Fixed_point_results_for_new_ contraction_involving_C-class_functions_in_partail_metric_spaces, 2017.
  23. H. Argoubi, B. Samet, C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl. 8 (2015), 1082-1094.
  24. S.G. Matthews, Partial metric topology. In Proceedings of the 8th Summer Conference on General Topology and Applications, Ann. N.Y. Acad. Sci. 728 (1994), 183-197.
  25. A. Chandaa, A. Ansari, L. Kanta Dey, B. Damjanovi`c. On Non-Linear Contractions via Extended CF-Simulation Functions. Filomat 32(10) (2018), 3731-3750
  26. A.H. Ansari. Note on φ - ψ-contractive type mappings and related fixed point. In: The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, pp. 377-380, 2014.
  27. A.F. Rold ´an-L ´opez-de-Hierro, B. Samet. φ-admissibility results via extended simulation functions. J. Fixed Point Theory Appl. 19(3) (2017), 1997-2015.