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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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).

© 2019 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)

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