Altering distance and common fixed points for hybrid mappings under implicit relations and applications
Abstract
In this paper we prove a general fixed point theorem by altering distance for two pairs of owc hybrid mappings generalizing the main result from [10] and we reduce the study of fixed point of pairs of mappings satisfying a contractive condition of integral type at the study of fixed points in metric spaces by altering distance satisfying an implicit relation.
Keywords
occasionally weakly compatible; occasionally converse commuting; fixed point; quasi-metric space; G-metric space
References
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21. Khan M.S., Swaleh M., Sessa S., Fixed point theorems by altering distances between two points, Bull. Austral. Math. Soc. 30 (1984), 1–9.
22. Kohli J.K., Washistha S., Common fixed point theorems for compatible and weakly compatible mappings satisfying a general contractive condition, Stud. Cerc. St. Ser. Mat. Univ. Bacău 16 (2006), 33–42.
23. Kumar S., Chug R., Kumar R., Fixed point theorems for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math. 33 (2007), 181–185.
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26. Popa V., Mocanu M., A new viewpoint in the study of fixed points for mappings satisfying a contractive condition of integral type, Bul. Inst. Politeh. Iaşi, Sect. Mat. Mec. Teor. Fiz. 53 (2007), 269–272.
27. Popa V., Mocanu M., Altering distance and common fixed points under implicit relations, Hacettepe J. Math. Stat. 38 (2009), 329–337.
28. Rhoades B.E., Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Intern. J. Math. Math. Sci. 15 (2005), 2359–2364.
29. Sastri K.P., Babu G.V.R., Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc. 90 (1998), 175–182.
30. Sastri K.P., Babu G.V.R., Some fixed point theorems by altering distances between points, Indian J. Pure Appl. Math. 30 (1999), 641–647.
31. Turkoglu D., Altun I., Fisher B., Common fixed point theorems for four mappings with some weak conditions of commutativity, Novi Sad J. Math. 30 (2006), 75–86.
2. Ahmed M., Common fixed point theorems for weakly compatible mappings, Rocky Mountain J. Math. 33 (2003), 1183–1203.
3. Aliouche A., A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type, J. Math. Anal. Appl. 322 (2006), 796–802.
4. Aliouche A., Popa V., General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math. 30 (2009), 89–109.
5. Altun I., Turkoglu D., Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation, Filomat 22 (2008), 13–23.
6. Altun I., Turkoglu D., Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanese J. Math. 13 (2009), 1291–1304.
7. Altun I., Turkoglu D., Rhoades B.E., Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007, Article ID 17301, 9 pp.
8. Al-Thagafi M.A., Shahzad N., Generalized I-non-expansive self maps and invariant approximation, Acta Math. Sinica 24 (2008), 867–876.
9. Bouhadjera H., Djoudi A., Common fixed point theorems for single valued and set valued maps, Anal. Univ. Oradea, Fasc. Matem. 15 (2008), 109–127.
10. Bouhadjera H., Godet-Thobie C., Common fixed point theorems for occasionally weakly compatible maps, Acta Math. Vietnamica 36 (2011), 1–17.
11. Branciari A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Intern. J. Math. Math. Sci 29 (2002), 531–536.
12. Djoudi A., Aliouche A., Common fixed point theorems of Greguš type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (2007), 31–45.
13. Djoudi A., Merghadi F., Common fixed point theorems for maps under a contractive condition of integral type, J. Math. Anal. Appl. 341 (2008), 953–960.
14. Elamrani M., Mehdaoui B., Common fixed point theorems for compatible and weakly compatible mappings, Revista Columbiana de Mateematicas 34 (2000), 25–33.
15. Fisher B., Common fixed point for mappings and set valued mappings, Rostok Math. Kolloq. 18 (1981), 69–77.
16. Fisher B., Sessa S., Two common fixed point theorems for weakly commuting mappings, Period. Math. Hungar. 20 (1989), 207–218.
17. Imdad M., Kumar S., Khan M.S., Remarks on some fixed points satisfying implicit relations, Radovi Mat. 11 (2002), 135–143.
18. Jungck G., Rhoades B.E., Some fixed point theorems for compatible mappings, Intern. J. Math. Math. Sci. 16 (1993), 417–428.
19. Jungck G., Rhoades B.E., Fixed point theorems for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), 227–238.
20. Jungck G., Rhoades B.E., Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7 (2006), 287–297.
21. Khan M.S., Swaleh M., Sessa S., Fixed point theorems by altering distances between two points, Bull. Austral. Math. Soc. 30 (1984), 1–9.
22. Kohli J.K., Washistha S., Common fixed point theorems for compatible and weakly compatible mappings satisfying a general contractive condition, Stud. Cerc. St. Ser. Mat. Univ. Bacău 16 (2006), 33–42.
23. Kumar S., Chug R., Kumar R., Fixed point theorems for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math. 33 (2007), 181–185.
24. Mocanu M., Popa V., Some fixed point theorems for mappings satisfying implicit relations in symmetric spaces, Libertas Math. 28 (2008), 1–13.
25. Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), 157–163.
26. Popa V., Mocanu M., A new viewpoint in the study of fixed points for mappings satisfying a contractive condition of integral type, Bul. Inst. Politeh. Iaşi, Sect. Mat. Mec. Teor. Fiz. 53 (2007), 269–272.
27. Popa V., Mocanu M., Altering distance and common fixed points under implicit relations, Hacettepe J. Math. Stat. 38 (2009), 329–337.
28. Rhoades B.E., Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Intern. J. Math. Math. Sci. 15 (2005), 2359–2364.
29. Sastri K.P., Babu G.V.R., Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc. 90 (1998), 175–182.
30. Sastri K.P., Babu G.V.R., Some fixed point theorems by altering distances between points, Indian J. Pure Appl. Math. 30 (1999), 641–647.
31. Turkoglu D., Altun I., Fisher B., Common fixed point theorems for four mappings with some weak conditions of commutativity, Novi Sad J. Math. 30 (2006), 75–86.
PopaV., & PatriciuA.-M. (2014). Altering distance and common fixed points for hybrid mappings under implicit relations and applications. Annales Mathematicae Silesianae, 28, 87-96. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13994
Valeriu Popa
vpopa@ub.ro
“Vasile Alecsandri” University of Bacău, Romania Romania
“Vasile Alecsandri” University of Bacău, Romania Romania
Alina-Mihaela Patriciu
“Vasile Alecsandri” University of Bacău, Romania Romania
“Vasile Alecsandri” University of Bacău, Romania Romania
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