AIMS Mathematics, 2020, 5(1): 342-358. doi: 10.3934/math.2020023

Research article

Export file:


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


  • Citation Only
  • Citation and Abstract

Integral type contractions of soft set-valued maps with application to neutral differential equations

Department of Mathematics, COMSATS University, Chak Shahzad, Islamabad, 44000, Pakistan

We establish e-soft fixed point results for soft set-valued maps under some integral contractive conditions on a complete metric space. Starting from Branciari integral contraction, the presented results are soft set extensions of many existing results on point-to-point and point-to-set mappings. In particular, the established idea herein improves the recently introduced concepts of soft set-valued maps. Moreover, examples and applications to nonlinear neutral differential equations are provided to support the usability of the derived results.
  Article Metrics


1. A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmetric spaces satsifying a contractive condition of integral type, J. Math. Anal. Appl., 322 (2006), 796-802.    

2. I. Altun, D. Turkoglu, Some fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type on d-complete topological spaces, Fasc. Math., 42 (2009), 5-15.

3. S. C. Arora, V. Sharma, Fixed point theorems for fuzzy mappings, Fuzzy Set. Syst., 110 (2000), 127-130.    

4. A. Azam, I. Beg, Common fixed points of fuzzy maps, Math. Comput. Model., 49 (2009), 1331-1336.    

5. A. Azam, M. Arshad, I. Beg, Fixed points of fuzzy contractive and fuzzy locally contractive maps, Chaos. Soliton. Fract., 42 (2009), 2836-2841.    

6. A. Azam, M. Arshad, P. Vetro, On a pair of fuzzy ψ-contractive mappings, Math. Comput. Model., 52 (2010), 207-214.    

7. S. Banach, Sur les opérations dans les esembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181.    

8. M. Bachar, M. A. Khamsi, Delay differential equations: A partially ordered sets approach in vectorial metric spaces, Fixed Point Theory A., 2014 (2014), 193.

9. M. Beygmohammadi, A. Razani, Two fixed point theorems for mappings satisfying a general contractive condition of integral type in modular space, Int. J. Math. Math. Sci., 2010 (2010), 317107.

10. R. K. Bose, D. Sahani, Fuzzy mappings and fixed point theorems, Fuzzy Set. Syst., 21 (1987), 53-58.    

11. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536.    

12. D. Butnairu, Fixed point for fuzzy mapping, Fuzzy Set. Syst., 7 (1982), 191-207.    

13. N. Cagman, S. Karatas, S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011), 351-358.    

14. A. Djoudi, R. Khemis, Fixed point techniques and stability for neutral nonlinear differential equations with unbounded delays, Georgian Math. J., 13 (2006), 25-34.    

15. F. Fatimah, D. Rosadi, R. F. Hakim, et al. N-soft sets and their decision making algorithms, Soft Comput., 22 (2018), 3829-3842.    

16. S. Heilpern, Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl., 83 (1981), 566-569.    

17. T. L. Hicks, B. E. Rhoades, Fixed point theorems for d-complete topological spaces, Int. J. Math. Math. Sci., 37 (1992), 847-853.

18. J. Jachymski, Remarks on contractive conditions of integral type, Theory Met. Appl., 71 (2009), 1073-1081.    

19. M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, B. Aust. Math. Soc., 30 (1984), 1-9.    

20. M. A. Khamsi, Quasi contraction mappings in modular spaces without2-contraction, Fixed Point Theory A., 2008 (2008), 916187.

21. S. Mila, L. Gajic, D. Tatjana, et al. Fixed point of multivalued integral type of contraction mappings, Fixed Point Theory A., 2015 (2015), 146.

22. S. Molodtsov, Soft set theory, Comput. Math. Appl., 37 (1999), 19-31.

23. P. Murthy, P. Kumam, S. Tas, Common fixed points of self maps satisfying an integral type contractive conditions in fuzzy metric spaces, Math. Commun., 15 (2010), 521-537.

24. S. B. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969), 475-488.    

25. B. E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 63 (2003), 4007-4013.

26. M. Riaz, N. Çagman, I. Zareef, et al. N-soft topology and its applications to multi-criteria group decision making, J. Intell. Fuzzy Syst., 36 (2019), 6521-6536.    

27. M. R. Taskovic, Some new principles in fixed point theory, Math. Japonica., 35 (1990), 645-666.

28. M. S. Shagari, A. Azam, Fixed points of soft-set valued and fuzzy set-valued maps with applications, J. Intell. Fuzzy Syst., 37 (2019), 3865-3877.    

29. M. D. Weiss, Fixed points and induced fuzzy topologies for fuzzy sets, J. Math. Anal. Appl., 50 (1975), 142-150.    

30. L. Zadeh, Fuzzy sets, Inf. Contr., 8 (1965), 338-353.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved