Some generalizations of non-unique fixed point theorems of Ćirić-type for (Φ,ψ)-hybrid contractive mappings
Abstract
In this article, we establish some non-unique fixed point theorems of Ćirić’s type for (Φ,ψ)-hybrid contractive mappings by using a similar notion to that of the paper [M. Akram, A.A. Zafar and A.A. Siddiqui, A general class of contractions: A-contractions, Novi Sad J. Math. 38 (2008), no. 1, 25–33]. Our results generalize, extend and improve several ones in the literature.
Keywords
non-unique fixed point theorems of Ćirić; general class of contractions; (Φ,ψ)-hybrid contractive mappings
References
1. J. Achari, On Ćirić's non-unique fixed points, Mat. Vesnik 13(28) (1976), no. 3, 255–257.
2. J. Achari, Results on nonunique fixed points, Publ. Inst. Math. (Beograd) (N.S.) 26(40) (1979), 5–9.
3. J. Achari, On the generalization of Pachpatte's nonunique _xed point theorem, Indian J. Pure Appl. Math. 13 (1982), no. 3, 299–302.
4. R.P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge University Press, Cambridge, 2001.
5. M. Akram, A.A. Zafar and A.A. Siddiqui, A general class of contractions: A-contractions, Novi Sad J. Math. 38 (2008), no. 1, 25–33.
6. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.
7. V. Berinde, Iterative approximation of fixed points, Editura Efemeride, Baia Mare, 2002.
8. V. Berinde, Iterative approximation of fixed points, Second edition, Springer, Berlin, 2007.
9. A. Branciari, A fixed point theorem for mappings satisfying a general contractive conditio of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531–536.
10. S.K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727–730.
11. L.B. Ćirić, On contraction type mappings, Math. Balkanica 1 (1971), 52–57.
12. L.B. Ćirić, On some maps with a nonunique fixed point, Publ. Inst. Math. (Beograd) (N.S.) 17(31) (1974), 52–58.
13. L.B. Ćirić, Some Recent Results in Metrical Fixed Point Theory, University of Belgrade, Belgrade, 2003.
14. L.B. Ćirić and N. Jotić, A further extension of maps with non-unique fixed points, Mat. Vesnik 50 (1998), no. 1–2, 1–4.
15. D.S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), no. 2, 223–230.
16. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71–76.
17. E. Karapınar, Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstr. Appl. Anal. 2010, Art. ID 123094, 14 pp.
18. M.A. Khamsi and W.A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Wiley-Interscience, New York, 2001.
19. M.G. Maia, Un'osservazione sulle contrazioni metriche, Rend. Sem. Mat. Univ. Padova, 40 (1968), 139–143.
20. M.O. Olatinwo, Some new fixed point theorems in complete metric spaces, Creat. Math. Inform. 21 (2012), no. 2, 189–196.
21. M.O. Olatinwo, Some Banach type fixed point theorems and implicit type error estimates, Kochi J. Math. 8 (2013), 105–117.
22. M.O. Olatinwo, Non-unique fixed point theorems of Ciric's type for rational hybrid contractions, Nanjing Daxue Xuebao Shuxue Bannian Kan 31 (2014), no. 2, 140–149.
23. M.O. Olatinwo, Some Ciric's type non-unique fixed point theorems and rational type contractive conditions, Kochi J. Math. 10 (2015), 1–9.
24. M.O. Olatinwo, Non-unique fixed point theorems of Achari and Ćirić-Jotić types for hybrid contractions, J. Adv. Math. Stud. 9 (2016), no. 2, 226–234.
25. M.O. Olatinwo, Some stability and convergence results for Picard, Mann, Ishikawa and Jungck type iterative algorithms for Akram-Zafar-Siddiqui type contraction mappings, Nonlinear Anal. Forum 21 (2016), no. 1, 65–75.
26. M.O. Olatinwo, Some non-unique fixed point theorems of Ćirić type using rational-type contractive conditions, Georgian Math. J. 24 (2017), no. 3, 455–461.
27. B.G. Pachpatte, On Ćirić type maps with a nonunique fixed point, Indian J. Pure Appl. Math. 10 (1979), no. 8, 1039–1043.
28. B.E. Rhoades, Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2003, no. 63, 4007_4013.
29. I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj–Napoca, 2001.
30. I.A. Rus and A. Petruşel, G. Petruşel, Fixed Point Theory: 1950_2000. Romanian Contributions, House of the Book of Science, Cluj–Napoca, 2002.
31. T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel) 23 (1972), 292–298.
32. E. Zeidler, Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems, Springer-Verlag, New York, 1986.
2. J. Achari, Results on nonunique fixed points, Publ. Inst. Math. (Beograd) (N.S.) 26(40) (1979), 5–9.
3. J. Achari, On the generalization of Pachpatte's nonunique _xed point theorem, Indian J. Pure Appl. Math. 13 (1982), no. 3, 299–302.
4. R.P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge University Press, Cambridge, 2001.
5. M. Akram, A.A. Zafar and A.A. Siddiqui, A general class of contractions: A-contractions, Novi Sad J. Math. 38 (2008), no. 1, 25–33.
6. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.
7. V. Berinde, Iterative approximation of fixed points, Editura Efemeride, Baia Mare, 2002.
8. V. Berinde, Iterative approximation of fixed points, Second edition, Springer, Berlin, 2007.
9. A. Branciari, A fixed point theorem for mappings satisfying a general contractive conditio of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531–536.
10. S.K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727–730.
11. L.B. Ćirić, On contraction type mappings, Math. Balkanica 1 (1971), 52–57.
12. L.B. Ćirić, On some maps with a nonunique fixed point, Publ. Inst. Math. (Beograd) (N.S.) 17(31) (1974), 52–58.
13. L.B. Ćirić, Some Recent Results in Metrical Fixed Point Theory, University of Belgrade, Belgrade, 2003.
14. L.B. Ćirić and N. Jotić, A further extension of maps with non-unique fixed points, Mat. Vesnik 50 (1998), no. 1–2, 1–4.
15. D.S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), no. 2, 223–230.
16. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71–76.
17. E. Karapınar, Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstr. Appl. Anal. 2010, Art. ID 123094, 14 pp.
18. M.A. Khamsi and W.A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Wiley-Interscience, New York, 2001.
19. M.G. Maia, Un'osservazione sulle contrazioni metriche, Rend. Sem. Mat. Univ. Padova, 40 (1968), 139–143.
20. M.O. Olatinwo, Some new fixed point theorems in complete metric spaces, Creat. Math. Inform. 21 (2012), no. 2, 189–196.
21. M.O. Olatinwo, Some Banach type fixed point theorems and implicit type error estimates, Kochi J. Math. 8 (2013), 105–117.
22. M.O. Olatinwo, Non-unique fixed point theorems of Ciric's type for rational hybrid contractions, Nanjing Daxue Xuebao Shuxue Bannian Kan 31 (2014), no. 2, 140–149.
23. M.O. Olatinwo, Some Ciric's type non-unique fixed point theorems and rational type contractive conditions, Kochi J. Math. 10 (2015), 1–9.
24. M.O. Olatinwo, Non-unique fixed point theorems of Achari and Ćirić-Jotić types for hybrid contractions, J. Adv. Math. Stud. 9 (2016), no. 2, 226–234.
25. M.O. Olatinwo, Some stability and convergence results for Picard, Mann, Ishikawa and Jungck type iterative algorithms for Akram-Zafar-Siddiqui type contraction mappings, Nonlinear Anal. Forum 21 (2016), no. 1, 65–75.
26. M.O. Olatinwo, Some non-unique fixed point theorems of Ćirić type using rational-type contractive conditions, Georgian Math. J. 24 (2017), no. 3, 455–461.
27. B.G. Pachpatte, On Ćirić type maps with a nonunique fixed point, Indian J. Pure Appl. Math. 10 (1979), no. 8, 1039–1043.
28. B.E. Rhoades, Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2003, no. 63, 4007_4013.
29. I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj–Napoca, 2001.
30. I.A. Rus and A. Petruşel, G. Petruşel, Fixed Point Theory: 1950_2000. Romanian Contributions, House of the Book of Science, Cluj–Napoca, 2002.
31. T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel) 23 (1972), 292–298.
32. E. Zeidler, Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems, Springer-Verlag, New York, 1986.
OlatinwoM. O. (2019). Some generalizations of non-unique fixed point theorems of Ćirić-type for (Φ,ψ)-hybrid contractive mappings. Annales Mathematicae Silesianae, 33, 221-234. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13669
Memudu O. Olatinwo
memudu.olatinwo@gmail.com
Department of Mathematics, Obafemi Awolowo University, Nigeria Nigeria
Department of Mathematics, Obafemi Awolowo University, Nigeria Nigeria
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