A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

Popa, Valeriu

doi:10.1515/amsil-2015-0009

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.

References

[1] Altun I., Turkoglu D., Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanese J. Math. 13 (2009), no. 4, 1291–1304.
Search in Google Scholar
[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.10.1155/2010/621469
Search in Google Scholar
[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.
Search in Google Scholar
[4] Chatterjee S., Fixed point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727–730.
Search in Google Scholar
[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.
Search in Google Scholar
[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.10.1186/1687-1812-2013-38
Search in Google Scholar
[7] Hardy G.E., Rogers T.D., A generalization of a fixed point of Reich, Can. Math. Bull. 16 (1973), no. 2, 201–206.
Search in Google Scholar
[8] Kannan R., Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71–76.
Search in Google Scholar
[9] Karapinar E., Fixed point theory for cyclic weak ϕ-contraction, Appl. Math. Lett. 24 (2011), no. 6, 822–825.
Search in Google Scholar
[10] Karapinar E., Erhan I.M., Cyclic contractions and fixed point theorems, Filomat 26 (2012), no. 4, 777–782.
Search in Google Scholar
[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.
Search in Google Scholar
[12] Nadler S.B., Multivalued contraction mappings, Pacific J. Math. 20 (1969), no. 2, 457–488.
Search in Google Scholar
[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.10.1155/2012/386253
Search in Google Scholar
[14] Păcurar M., Fixed point theory for cyclic Berinde operators, Fixed Point Theory 12 (2011), no. 2, 419–428.
Search in Google Scholar
[15] Păcurar M., Rus I.A., Fixed point theory for cyclic φ-contractions, Nonlinear Anal. 72 (2010), 1181–1187.10.1016/j.na.2009.08.002
Search in Google Scholar
[16] Petric M.A., Some results concerning cyclical contractive mappings, Gen. Math. 18 (2010), no. 4, 213–226.
Search in Google Scholar
[17] Popa V., Some fixed point theorems for implicit contractive mappings, Stud. Cercet. Ştiinţ., Ser. Mat., Univ. Bacău 7 (1997), 129–133.
Search in Google Scholar
[18] Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157–163.
Search in Google Scholar
[19] Popa V., A general fixed point theorem for weakly commuting multi-valued mappings, Anal. Univ. Dunărea de Jos, Galaţi, Ser. Mat. Fiz. Mec. Teor., Fasc. II 18 (22) (1999), 19–22.
Search in Google Scholar
[20] Popa V., A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33 (2000), no. 1, 159–164.
Search in Google Scholar
[21] Reich S., Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121–124.10.4153/CMB-1971-024-9
Search in Google Scholar
[22] Rus I.A., Cyclic representations of fixed points, Ann. Tiberiu Popoviciu, Semin. Funct. Equ. Approx. Convexity 3 (2005), 171–178.
Search in Google Scholar
[23] Sintunavarat W., Kumam P., Common fixed point theorem for cyclic generalized multi-valued mappings, Appl. Math. Lett. 25 (2012), 1849–1855.10.1016/j.aml.2012.02.045
Search in Google Scholar

A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

Abstract

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