Some Common Fixed Point Results For Contractive Mappings In Ordered Gp-Metric Spaces

Yıl 2016, Cilt: 15 Sayı: 30, 1 - 34, 31.12.2016

Meltem Kaya , Hasan Furkan

Öz

In this present
article, the sufficient conditions for the existence and uniqueness of  fixed points and common fixed points of single
and double mappings satisfying various contractive conditions within the
partially ordered Gp














-complete Gp
-metric spaces have been obtained.  Also, some examples supporting  the  results
obtained  have  been given.  The theorems obtained  generalize some fixed point results existing
in the literatüre.

Anahtar Kelimeler

gp

Kısmi Sıralı Gp Metrik Uzaylarda Daralma Dönüşümleri İçin Bazı Ortak Sabit Nokta Sonuçları

Öz

Bu
çalışmada, kısmi sıralı Gp














-tam Gp
-metrik uzaylarda çeşitli daralma şartlarını sağlayan  tek ve çift dönüşümlerin sabit noktalarının ve
ortak sabit noktalarının varlığı ve tekliği için gerekli olan şartlar elde edilmiştir.
Aynı zamanda, elde edilen sonuçları destekleyen birkaç örnek verilmiştir. Elde
edilen teoremler literatürde bulunan bazı sabit nokta sonuçlarını genelleştirir

Anahtar Kelimeler

som

Kaynakça

• Altun, I., Erduran, A., (2010), ``Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces’’, Fixed Point Theory Appl., 2011, 1–10.
• Altun, I., Sola F., Şimşek, H. (2010), ``Generalized contractions on partial metric spaces’’, Topology Appl., 157, 2778–2785.
• Altun, I, Şimşek, H., (2010), ``Some Fixed Point Theorems on Ordered Metric Spaces and Application’’, Fixed Point Theory and Applications, 2010, 17 pages .
• Aydi, H., Karapınar E., Salimi, P., (2012), ``Some fixed point results in -metric spaces’’, J. Appl. Math., 2012, 1–15.
• Banach, S., (1922), ``Sur les operations dans les ensembles abstraits et leur application aux équations integrales’’, Fund. Math. J., 3, 133–181.
• Barakat M.A., Zidan, A.M. (2015), ``A common fixed point theorem for weak contractive maps in -metric spaces’’, J. Egyptian Math. Soc., 23, 309–314.
• Beiranvand, A., Moradi, S., Omid, M., Pazandeh, H., (2009), ``Two Fixed Point Theorems For Special Mappings’’, arxiv:0903.1504v1 math.FA.
• Bilgili, N., Karapınar E., Salimi, P., (2013), ``Fixed point theorems for generalized contractions on -metric spaces’’, Journal of Inequalities and Applications 2013:39, 1–13.
• Chen, J., Li, Z., (2007) ``Common Fixed Points For Banach Operator Pairs in Best Approximation’’, J. Math. Anal. Appl., 336, 1466–1475.
• Ciric, Lj., Alsulami, S. M., Parvaneh, V., Roshan, R., (2013), ``Some fixed point results in ordered -metric spaces’’, Fixed Point Theory Appl. 2013:317, 1–25.
• Harjani, J., Sadarangani, K., (2009), ``Fixed point theorems for weakly contractive mappings in partially ordered sets’’, Nonlinear Anal., 71, 3403-3410.
• Karapınar, E., (2011), ``Generalizations of Caristi Kirk’ s Theorem on Partial Metric Spaces’’, Fixed Point Theory Appl., 2011, 1–7.
• Kaya, M., Öztürk M., Furkan, H., ``Some Common Fixed Point Theorems for -Contraction Mappings in - -Complete -Metric Spaces’’, British Journal of Mathematics & Computer Science, 16(2), 1--23, (2016)
• Matthews, S.G., (1994), ``Partial metric topology’’, in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728, 183–197.
• Mustafa, Z., Sims, B., (2006), ``A new approach to generalized metric spaces’’, J. Nonlinear Convex Anal., 7, 289–297.
• Nieto, J.J., López, R.R., (2005) ``Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations’’, Order. 22, 223–239.
• Oltra S., Valero, O., (2004), ``Banachs fixed point theorem for partial metric spaces’’, Rend. Istit. Math. Univ. Trieste, 36, 17–26.
• Parvaneh, V., Roshan, J.R., Kadelburg, Z., (2013), ``On generalized weakly -contractive mappings in ordered -metric spaces’’, Gulf J. Math., 1, 78–97.
• Parvaneh, V., Salimi, P., Vetro, P., Nezhad A.D., Radenović, S., (2014), ``Fixed point results for -contractive mappings’’, J. Nonlinear Sci. Appl., 7, 150–159.
• Popa, V., Patriciu, A. M., (2015), ``Two general fixed point theorems for a sequence of mappings satisfying implicit relations in -metric spaces’’, Appl. Gen. Topol. 16, 225-231.
• Ran, A.C.M., Reurings, M.C.B., (2003), ``A fixed point theorem in partially ordered sets and some applications to matrix equations’’, Proc. Amer. Math. Soc. 132, 1435–1443.
• Salimi, P., Vetro, P., (2014), ``A result of Suzuki type in partial -metric spaces’’, Acta Mathematica Scientia, 34B (2):274-284.
• Schellekens, M.P., (2003), ``A characterization of partial metrizability: domains are quantifiable’’, Theoret. Comp. Sci., 305,. 409–432 .
• Valero, O., (2005), ``On Banach fixed point theorems for partial metric spaces’’, Appl. Gen. Topol., 6, 229–240.
• Zand, M.R.A., Nezhad, A.D., (2011), ``A generalization of partial metric spaces’’, J. Contemp. Appl. Math., 24, 86–93.