A general fixed point theorem for implicit cyclic multi-valued contraction mappings
Abstract
In this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15], [13], [14], [16], [10] and from other papers, is proved.
Keywords
fixed point; multi-valued function; cyclical contraction; implicit relation
References
2. Altun I., Simsek H., Some fixed point theorems on ordered metric spaces and applications, Fixed Point Theory Appl. 2010, Art. ID 621469, 17 pp.
3. Aydi H., Jellali M., Karapinar E., Common fixed points for generalized α-implicit contractions in partial metric spaces: Consequences and application, RACSAM–Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. To appear.
4. Chatterjee S., Fixed point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727–730.
5. Gulyaz S., Karapinar E., Coupled fixed point result in partially ordered partial metric spaces through implicit function, Hacet. J. Math. Stat. 42 (2013), no. 4, 347–357.
6. Gulyaz S., Karapinar E., Yuce I.S., A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation, Fixed Point Theory Appl. 2013, 2013: 38, 11 pp.
7. Hardy G.E., Rogers T.D., A generalization of a fixed point of Reich, Can. Math. Bull. 16 (1973), no. 2, 201–206.
8. Kannan R., Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71–76.
9. Karapinar E., Fixed point theory for cyclic weak ϕ-contraction, Appl. Math. Lett. 24 (2011), no. 6, 822–825 .
10. Karapinar E., Erhan I.M., Cyclic contractions and fixed point theorems, Filomat 26 (2012), no. 4, 777–782.
11. Kirk W.A., Srinivasan P.S., Veeramani P., Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (2003), no. 1, 79–89.
12. Nadler S.B., Multivalued contraction mappings, Pacific J. Math. 20 (1969), no. 2, 457–488.
13. Nashine H.K., Kadelburg Z., Kumam P., Implicit-relation-type cyclic contractive mappings and applications to integral equations, Abstr. Appl. Anal. 2012, Art. ID 386253, 15 pp.
14. Păcurar M., Fixed point theory for cyclic Berinde operators, Fixed Point Theory 12 (2011), no. 2, 419–428.
15. Păcurar M., Rus I.A., Fixed point theory for cyclic φ-contractions, Nonlinear Anal. 72 (2010), 1181–1187.
16. Petric M.A., Some results concerning cyclical contractive mappings, Gen. Math. 18 (2010), no. 4, 213–226.
17. Popa V., Some fixed point theorems for implicit contractive mappings, Stud. Cercet. Științ., Ser. Mat., Univ. Bacău 7 (1997), 129–133.
18. Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157–163.
19. Popa V., A general fixed point theorem for weakly commuting multi-valued mappings, Anal. Univ. Dunărea de Jos, Galați, Ser. Mat. Fiz. Mec. Teor., Fasc. II 18 (22) (1999), 19–22.
20. Popa V., A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33 (2000), no. 1, 159–164.
21. Reich S., Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121–124.
22. Rus I.A., Cyclic representations of fixed points, Ann. Tiberiu Popoviciu, Semin. Funct. Equ. Approx. Convexity 3 (2005), 171–178.
23. Sintunavarat W., Kumam P., Common fixed point theorem for cyclic generalized multi-valued mappings, Appl. Math. Lett. 25 (2012), 1849–1855.
“Vasile Alecsandri” University of Bacău, Romania Romania
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