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

• Autorzy: Valeriu Popa
• Języki publikacji: EN

Abstrakty

EN

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.(original abstract)

Słowa kluczowe

EN

Mathematics; Differential equations

PL

Matematyka; Równania różniczkowe

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Strony: 119--129

Twórcy

autor

Valeriu Popa

• Vasile Alecsandri" University of Bacau

Bibliografia

• 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.
• Altun I., Simsek H., Some fixed point theorems on ordered metric spaces and applications, Fixed Point Theory Appl. 2010, Art. ID 621469, 17 pp.
• Aydi H., Jellali M., Karapinar E., Common fixed points for generalized -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.
• Chatterjee S., Fixed point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727-730.
• 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.
• 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.
• Hardy G.E., Rogers T.D., A generalization of a fixed point of Reich, Can. Math. Bull. 16 (1973), no. 2, 201-206.
• Kannan R., Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71-76.
• Karapinar E., Fixed point theory for cyclic weak -contraction, Appl. Math. Lett. 24 (2011), no. 6, 822-825 .
• Karapinar E., Erhan I.M., Cyclic contractions and fixed point theorems, Filomat 26 (2012), no. 4, 777-782.
• 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.
• Nadler S.B., Multivalued contraction mappings, Pacific J. Math. 20 (1969), no. 2, 457- 488.
• 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.
• Pacurar M., Fixed point theory for cyclic Berinde operators, Fixed Point Theory 12 (2011), no. 2, 419-428.
• Pacurar M., Rus I.A., Fixed point theory for cyclic '-contractions, Nonlinear Anal. 72 (2010), 1181-1187.
• Petric M.A., Some results concerning cyclical contractive mappings, Gen. Math. 18 (2010), no. 4, 213-226.
• Popa V., Some fixed point theorems for implicit contractive mappings, Stud. Cercet. Stiinµ., Ser. Mat., Univ. Bacau 7 (1997), 129-133.
• Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157-163.
• Popa V., A general fixed point theorem for weakly commuting multi-valued mappings, Anal. Univ. Dunarea de Jos, Galaµi, Ser. Mat. Fiz. Mec. Teor., Fasc. II 18 (22) (1999), 19-22.
• Popa V., A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33 (2000), no. 1, 159-164.
• Reich S., Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121-124.
• Rus I.A., Cyclic representations of fixed points, Ann. Tiberiu Popoviciu, Semin. Funct. Equ. Approx. Convexity 3 (2005), 171-178.
• Sintunavarat W., Kumam P., Common fixed point theorem for cyclic generalized multivalued mappings, Appl. Math. Lett. 25 (2012), 1849-1855.

Identyfikatory

DOI

10.1515/amsil-2015-0009