Year 2013,
Volume: 26 Issue: 1, 39 - 45, 31.03.2013
Erdal Karapinar
,
Fridoun Moradlou
,
Peyman Salimi
References
- Banach, S., “Sur les operations dans les ensembles abstraits et leur application aux equations itegrales”, Fund. Math., 3(1922)133–181.
- Huang, L. G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl. 332 (2007), 1468–1476.
- Fréchet, M., “Sur quelques points du calcul fonctionnel”, Rend. Circ. Mat. Palermo 22 (1906) 1–-74.
- Zabrejko, P. P., “K-metric and K-normed linear spaces: survey”, Collect. Math. 48 (1997), 825– 859.
- Kurepa, D. R., “Tableaux ramifiés d’ensembles. Espace pseudo-distanciés”, Comptes Rendus l’Académie des Sciences, 198,(1934) 1563–1565.
- Krein, M. G., Rutman, M. A., “Linear operators leaving invariant a cone in a Banach space”, Uspekhi Matematicheskikh Nauk,3(1),(1948) 3– 95.
- Kantorovic, L. V., “The principle of the majorant and Newton’s method”, Doklady Akademii Nauk SSSR, 76(1951) 17–20.
- Rzepecki, B., “On fixed point theorems of Maia type”, Publications De L’institut Mathématique 28 (1980), 179–-186.
- Lin, S. D., “A common fixed point theorem in abstract spaces”, Indian J. Pure Appl. Math. 18 (8) (1987) 685–690.
- Abdeljawad, T., Karapnar, E., “Quasi-Cone Metric Spaces and Generalizations of Caristi Kirk’s Theorem”, doi:10.1155/2009/574387 (2009). Theory Appl.
- Abdeljawad, T., “Completion of cone metric spaces”, Hacet. J. Math. Stat., (to appear).
- Abdeljawad, T., Karapınar, E., “A Common Fixed Point Theorem of a Gregus Type on Convex Cone Metric Spaces”, J. Comput. Anal. Appl. ,13(4), 609-621(2011).
- Abdeljawad, T., Turkoglu, D., Abuloha, M., “Some theorems and examples of cone Banach spaces”, J. Comput. Anal. Appl., 12(4), 739-753 (2010).
- Abdeljawad, T., Karapınar, E., Tas, K., “Common fixed point theorems in cone banach spaces”, Hacet. J. Math. Stat. 40 (2) (2011), 211–217.
- Cvetkovic, A. S., Stanic, M. P., Dimitrijevic, S., Simic, S., “Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space”, Fixed point Theory Appl. 15 pages (2011) Article ID 589725.
- Ding, H.-S., Kadelburg, Z., Karapınar, E., Radenovic, S., “Common Fixed Points of Weak Contractions in Cone Metric Spaces”, Abstr. Appl. Anal., 2012 2012 Article id: 793862
- Karapinar, E., “Fixed point theorems in cone Banach spaces”, Fixed Point Theory and Appl. 9 pages (2009) Article ID 60928.
- Karapinar, E., Yuksel, U., “On Common Fixed Point Theorems Without Commuting Conditions in tvs-Cone Metric Spaces”, J. Comput. Anal. Appl ,13(6), 1115-1122 (2011)
- E. Karapınar, Some Nonunique Fixed Point Theorems of Ciric type on Cone Metric Spaces, Abstr. Appl. Anal., vol. 2010, Article ID 123094, 14 pages (2010).
- Karapınar, E., “Couple Fixed Point Theorems For Nonlinear Contractions in Cone Metric Spaces”, Comput. Math. Appl. , 59( 12), , Pages 3656–3668 (2010).
- Karapınar, E., Türkoğlu, Approximations Theorem For a Couple in Cone Banach Space”, Fixed Point Theory Appl., Volume 2010 (2010), Article ID 784578, 9 pages.
- Rezapour, Sh., Hamlbarani, R., “Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings"”, J. Math. Anal. Appl. 347 (2008), 719–724.
- Sonmez, A., “On paracompactness in cone metric spaces”, Applied Mathematics Letters 23 (2010) 494, 497.
- Türkoğlu, D., Abuloha, “Cone metric spaces and fixed point theorems in diametrically contractive mappings”, Acta. Math. Sin. 26 (3) (2010), 489– 496.
- Türkoğlu, D., Abuloha, M., “Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings”, Acta Mathematica Sinica, English Series, 26(3), 489-496 (2010).
- Turkoglu, D., Abuloha, M., Abdeljawad, T., “KKM mappings in cone metric spaces and some fixed point theorems”, Nonlinear Analysis: Theory, Methods & Applications, 72(1), 348-353 (2010).
Common Fixed Point Theorem for Three Mappings in Banach Valued Norm Spaces
Year 2013,
Volume: 26 Issue: 1, 39 - 45, 31.03.2013
Erdal Karapinar
,
Fridoun Moradlou
,
Peyman Salimi
Abstract
In this paper, we give a generalized theorem on point of coincidence and common fixed point for three weakly compatiblemappings in Banach valued norm spaces. We give a new method for
construction of the sequence, which is convergence to the common fixed point of these three mappings.
References
- Banach, S., “Sur les operations dans les ensembles abstraits et leur application aux equations itegrales”, Fund. Math., 3(1922)133–181.
- Huang, L. G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl. 332 (2007), 1468–1476.
- Fréchet, M., “Sur quelques points du calcul fonctionnel”, Rend. Circ. Mat. Palermo 22 (1906) 1–-74.
- Zabrejko, P. P., “K-metric and K-normed linear spaces: survey”, Collect. Math. 48 (1997), 825– 859.
- Kurepa, D. R., “Tableaux ramifiés d’ensembles. Espace pseudo-distanciés”, Comptes Rendus l’Académie des Sciences, 198,(1934) 1563–1565.
- Krein, M. G., Rutman, M. A., “Linear operators leaving invariant a cone in a Banach space”, Uspekhi Matematicheskikh Nauk,3(1),(1948) 3– 95.
- Kantorovic, L. V., “The principle of the majorant and Newton’s method”, Doklady Akademii Nauk SSSR, 76(1951) 17–20.
- Rzepecki, B., “On fixed point theorems of Maia type”, Publications De L’institut Mathématique 28 (1980), 179–-186.
- Lin, S. D., “A common fixed point theorem in abstract spaces”, Indian J. Pure Appl. Math. 18 (8) (1987) 685–690.
- Abdeljawad, T., Karapnar, E., “Quasi-Cone Metric Spaces and Generalizations of Caristi Kirk’s Theorem”, doi:10.1155/2009/574387 (2009). Theory Appl.
- Abdeljawad, T., “Completion of cone metric spaces”, Hacet. J. Math. Stat., (to appear).
- Abdeljawad, T., Karapınar, E., “A Common Fixed Point Theorem of a Gregus Type on Convex Cone Metric Spaces”, J. Comput. Anal. Appl. ,13(4), 609-621(2011).
- Abdeljawad, T., Turkoglu, D., Abuloha, M., “Some theorems and examples of cone Banach spaces”, J. Comput. Anal. Appl., 12(4), 739-753 (2010).
- Abdeljawad, T., Karapınar, E., Tas, K., “Common fixed point theorems in cone banach spaces”, Hacet. J. Math. Stat. 40 (2) (2011), 211–217.
- Cvetkovic, A. S., Stanic, M. P., Dimitrijevic, S., Simic, S., “Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space”, Fixed point Theory Appl. 15 pages (2011) Article ID 589725.
- Ding, H.-S., Kadelburg, Z., Karapınar, E., Radenovic, S., “Common Fixed Points of Weak Contractions in Cone Metric Spaces”, Abstr. Appl. Anal., 2012 2012 Article id: 793862
- Karapinar, E., “Fixed point theorems in cone Banach spaces”, Fixed Point Theory and Appl. 9 pages (2009) Article ID 60928.
- Karapinar, E., Yuksel, U., “On Common Fixed Point Theorems Without Commuting Conditions in tvs-Cone Metric Spaces”, J. Comput. Anal. Appl ,13(6), 1115-1122 (2011)
- E. Karapınar, Some Nonunique Fixed Point Theorems of Ciric type on Cone Metric Spaces, Abstr. Appl. Anal., vol. 2010, Article ID 123094, 14 pages (2010).
- Karapınar, E., “Couple Fixed Point Theorems For Nonlinear Contractions in Cone Metric Spaces”, Comput. Math. Appl. , 59( 12), , Pages 3656–3668 (2010).
- Karapınar, E., Türkoğlu, Approximations Theorem For a Couple in Cone Banach Space”, Fixed Point Theory Appl., Volume 2010 (2010), Article ID 784578, 9 pages.
- Rezapour, Sh., Hamlbarani, R., “Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings"”, J. Math. Anal. Appl. 347 (2008), 719–724.
- Sonmez, A., “On paracompactness in cone metric spaces”, Applied Mathematics Letters 23 (2010) 494, 497.
- Türkoğlu, D., Abuloha, “Cone metric spaces and fixed point theorems in diametrically contractive mappings”, Acta. Math. Sin. 26 (3) (2010), 489– 496.
- Türkoğlu, D., Abuloha, M., “Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings”, Acta Mathematica Sinica, English Series, 26(3), 489-496 (2010).
- Turkoglu, D., Abuloha, M., Abdeljawad, T., “KKM mappings in cone metric spaces and some fixed point theorems”, Nonlinear Analysis: Theory, Methods & Applications, 72(1), 348-353 (2010).