NEW RESULTS FOR α-GERAGHTY TYPE CONTRACTIVE MAPS WİTH SOME APPLICATIONS

Yıl 2016, Cilt: 29 Sayı: 3, 651 - 658, 30.09.2016

Esra Yolacan , Mehmet Kır

Öz

In this paper, we establish some coupled fixed point theorems for α-Geraghty type contractive mappings in the context of partially ordered metric spaces. Applying these results, we deduce fixed point results on metric spaces endowed with graph. Also, the effectiveness of our work is validated with the help of a suitable example.

Anahtar Kelimeler

fixed point, partially ordered set; Geraghty-type contractive; connected graph

with Some Applıcatıons

Öz

Kaynakça

• Bhaskar, TG, Lakshmikantham, V: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379-1393 (2006).
• Amini A. Harandi, A, Emami, H: A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. Nonlinear Anal. 72, 2238-2242 (2010).
• Karapınar and Agarwal: A note on "Coupled fixed point theorems for α-ψ-contractive type mappings in partially ordered metric spaces". Fixed Point Theory and Applications 2013 2013: 216.
• M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973) 604-608.
• Mursaleen et al.: Coupled fixed point theorems for α-ψ-contractive type mappings in partially ordered metric spaces. Fixed Point Theory and Applications 2012 2012: 228.
• Samet, B, Vetro, C, Vetro, P: Fixed point theorems for α-ψ-contractive type mappings. Nonlinear Anal. 75, 2154-2165 (2012).
• Karapinar, E, Kumam, P, Salimi, P: On α-ψ-Meir-Keeler contractive type mappings. Fixed Point Theory and Applications 2013, Article ID 94 (2013).
• Banach, S: Sur les operations dans les ensembles abstraits et leur application aux equation integrales. Fund. Math. 3 (1922), 133-181.1.
• Rhoades, BE: A comprasion of various definitions of contractive mappings. Trans. Am. Math. Soc. 226 (1997), 257-290.
• Agarwal, RP, El-Gebeily, MA, O' Regan, D: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87 (2008), 1-8.
• Hille, E, Phillips, RS: Fuctional Analysis and Semi-Groups. Amer. Math. Soc. Colloq. Publ. 31 (1957). Am. Math. Soc., Providence.
• Huang, LG, Zhang, X: Cone metric space and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2) (2007), 1468-1476.
• Khamsi, MA, Kreinovich, VY: Fixed point theorems for dissipative mappings in complete probalistic metric spaces. Math. Jpn. 44 (1996), 513-50.
• Yang, SK, Bae, JS, Cho, SH: Coincidence and common fixed and periodic point theorems in cone metric spaces. Comput. Math. Appl. 61 (2011), 170-177.
• Popescu: Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces. Fixed Point Theory and Applications 2014, 2014: 190.
• Chuadchawna, P, Kaewcharoen, A, Plubtieng, S: Fixed point theorems for generalized and α-η-Geraghty contraction type mappings in α-η-complete metric spaces. J. Nonlinear Sci. Appl. 9 (2016), 471-485.
• Yolacan E, Some Fixed Point Theorems on generalized metric spaces, Asian journal of mathematics and appl.,vol. 2016, Article ID ama0294, 8 pages.
• Karapınar et al. α-(ψ,φ) Contractive mappings on quasi-partial metric space. Fixed Point Theory and Applications 2015, 2015: 105.
• Karapınar et al. Some extensions for Geragthy type contractive mappings. Journal of Inequalities and Applications 2015, 2015: 303.
• Chifu, C, Petrusel, G.: New results on coupled fixed point theorem in metric space endowed with a directed graph. Fixed Point Theory and Applications. 2014, 151 (2014).