AIMS Mathematics, 2019, 4(4): 1034-1045. doi: 10.3934/math.2019.4.1034.

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On $\mathcal{L}$-simulation mappings in partial metric spaces

1 Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
2 Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan
3 Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt
4 Department of Mathematics, College of Al Wajh, University of Tabuk, Saudi Arabia
5 University of Banja Luka, Faculty of Electrical Engineering, 78 000 Banja Luka, Bosnia and Herzegovina
6 Department of Mathematics, Aligarh Muslim University, 202002, Aligarh, India

The class of L-contractive mappings was introduced by Cho [12]. In this paper, we provide some fixed point results for such mappings via a control function introduced by Jleli and Samet [14] in the class of partial metric spaces. Some illustrating examples are given.
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Keywords partial metric space; fixed point; $\mathcal{L}$-simulation; $\theta$-function

Citation: Hassen Aydi, M. A. Barakat, Erdal Karapinar, Zoran D. Mitrović, Tawseef Rashid. On $\mathcal{L}$-simulation mappings in partial metric spaces. AIMS Mathematics, 2019, 4(4): 1034-1045. doi: 10.3934/math.2019.4.1034

References

  • 1. T. Abdeljawad, H. Aydi, E. Karapinar, Coupled fixed points for Meir-Keeler contractions in ordered partial metric spaces, Math. Probl. Eng., 2012 (2012).
  • 2. M. Abbas, B. Ali, C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topol. Appl., 160 (2013), 553-563.    
  • 3. P. Agarwal, M. A. Alghamdi, N. Shahzad, Fixed point theory for cyclic generalized contractions in partial metric spaces, Fixed Point Theory A., 2012 (2012), 40.
  • 4. I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory A., 2011 (2011), 508730.
  • 5. E. Ameer, H. Aydi, M. Arshad, et al. Hybrid multivalued type contraction mappings in αk-complete partial b-metric spaces and applications, Symmetry, 11 (2019), 86.
  • 6. H. Aydi, M. A. Barakat, Z. D. Mitrović, et al. A Suzuki type multi-valued contraction on weak partial metric spaces and application, J. Inequal. Appl., 2018 (2018), 270.
  • 7. H. Aydi, E. Karapinar, W. Shatanawi, Coupled fixed point results for (ψ,φ)-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl., 62 (2011), 4449-4460.    
  • 8. H. Aydi, E. Karapinar, New Meir-Keeler type tripled fixed point theorems on ordered partial metric spaces, Math. Probl. Eng., 2012 (2012), 1-17.
  • 9. H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topol. Appl., 159 (2012), 3234-3242.    
  • 10. B. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1992), 133-181.
  • 11. L. j. Ćirić, B. Samet, H. Aydi, et al. Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406.
  • 12. S. H. Cho, Fixed point theorems for $\mathcal{L}$-contractions in generalized metric spaces, Abstr. Appl. Anal., 2018 (2018), 1-6.
  • 13. S. Gulyaz, E. Karapinar, A coupled fixed point result in partially ordered partial metric spaces through implicit function, Hacet. J. Math. Stat., 42 (2013), 347-357.
  • 14. M. Jleli, B. Samet, new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 38.
  • 15. E. Karapınar, R. P. Agarwal, H. Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics, 6 (2018), 256.
  • 16. E. Karapinar, W. Shatanawi, K. Tas, Fixed point theorem on partial metric spaces involving rational expressions, Miskolc Math. Notes, 14 (2013), 135-142.    
  • 17. E. Karapinar, S. Romaguera, Nonunique fixed point theorems in partial metric spaces, Filomat, 27 (2013), 1305-1314.    
  • 18. E. Karapinar, I. Erhan, A. Ozturk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Model., 57 (2013), 2442-2448.    
  • 19. W. Kirk, N. Shahzad, Fixed point theory in distance spaces, Springer International Publishing, Switzerland, 2014.
  • 20. F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), 1189-1194.    
  • 21. S. G. Matthews, Partial metric topology, Ann. NY Acad. Sci., 728 (1994), 183-197.    
  • 22. S. J. O'Neill, Partial metrics, valuations and domain theory, Ann. NY Acad. Sci., 806 (1996), 304-315.    
  • 23. L. Pasicki, Dislocated quasi-metric and generalized contractions, Fixed Point Theory, 19 (2018), 359-368.    
  • 24. S. Radenović, Classical fixed point results in 0-complete partial metric spaces via cyclic-type extension, The Allahabad Mathematical Society, 31 (2016), 39-55.
  • 25. S. Radenović, Coincidence point results for generalized weakly (ψ,φ)-contractive mappings in ordered partial metric spaces, J. Indian Math. Soc., 3 (2014), 319-333.
  • 26. S. Romaguera, Fixed point theorems for generalized contraction on partial metric spaces, Topol. Appl., 159 (2012), 194-199.    
  • 27. W. Shatanawi, M. Postolache, Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces, Fixed Point Theory A., 2013 (2013), 54.
  • 28. W. Shatanawi, S. Manro, Fixed point results for cyclic (ψ,φ,A,B)-contraction in partial metric spaces, Fixed Point Theory A., 2012 (2012), 165.
  • 29. W. Shatanawi, H. K. Nashine, N. Tahat, Generalization of some coupled fixed point results on partial metric spaces, International Journal of Mathematics and Mathematical Sciences, 2012 (2012), 1-10.
  • 30. W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Model., 55 (2012), 680-687.    
  • 31. S. Shukla, S. Radenović, Some common fixed point theorems for $F$-contraction type mappings in 0-complete partial metric spaces, Journal of Mathematics, 2013 (2013).

 

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