Sıralı Düzgün Uzaylarda Lineer Olmayan Büzülmeler İçin İkili Sabit Nokta Teoremleri

Year 2019, Volume: 9 Issue: 1, 34 - 40, 01.01.2019

Demet Binbaşıoğlu

https://doi.org/10.7212/zkufbd.v9i1.1213

Abstract

Bu çalışmada, Altun and Imdad 2009 tarafından düzgün uzaylar üzerinde verilmiş olan sıralama bağıntısını kullanarak sıralı düzgün uzaylar üzerindeki iki dönüşüm için bazı ikili çakışık ve ikili ortak sabit nokta teoremleri ispat edilmiştir

Keywords

İkili sabit nokta, Lineer olmayan büzülmeler, Sıralı düzgün uzaylar

Coupled Fixed Point Theorems for Nonlinear Contractions in Ordered Uniform Spaces

Abstract

In this paper, we have proved some coupled coincidence and coupled common fixed point theorems for two mappings defined on the ordered uniform spaces by using the order relation on uniform spaces presented by Altun and Imdad 2009 .

Keywords

Coupled Fixed Point, Non-linear Contractions, Ordered Uniform Spaces

References

• Aamri, M., El Moutawakil, D. 2004. Common fixed point theorems for E- contractive or E-expansive maps in uniform spaces. .Acta Math. Acad. Pea. Nyir. ,20: 83-91.
• Aamri, M., El Moutawakil, D. 2005. Weak compatibility and common fixed point theorems for A-contractive and E-expansive maps in uniform spaces. Serdica Math. J.,31, 75- 86.
• Abbas, M., Ilic, D., Khan, MA. 2010. Coupled coincidence point and coupled common fixed point theorems in partially ordered metric spaces with w-distance. Fixed Point Theo. Appl.,Article ID:134897.
• Agarwal, RP., O’Regan, D., Papageorgiou, NS. 2004. Common fixed point theory for multivalued contractive maps of Reich type in uniform spaces. Appl. Anal.,83(1): 37-47.
• Agarwal, RP., El-Gebeily, MA., O’Regan, D. 2008. Generalized contractions in partially ordered metric spaces. Appl. Anal.,87: 109-116.
• Altun, I., Imdad, M. 2009. Some fixed point theorems on ordered uniform spaces. Filomat,23(3): 15-22.
• Bhaskar, TG. Lakshmikantham,V. 2006. Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal.,65: 1379-1393.
• Boyd, DW., Wong, JS. 1969. On nonlinear contractions. Proc. Amer. Math. Soc.,20: 458-464.
• Ciric, LB. 2008. Fixed point theorems for multi-valued contractions in complete metric spaces. J. Math. Anal. Appl.,348(1): 499-507.
• Guo, D., Lakshmikantham,V. 1987. Coupled fixed points of nonlinear operators with applications. Nonlinear Anal.,11, 623-632.
• Lakshmikantham, V., Ciric, LB. 2009. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal.,70: 4341-4349
• Nieto, JJ., Lopez, RR. 2005. Contractive mapping theorems in partially ordered sets and applications to ordinary diferential equations. Order, 22: 223-239.
• Nieto, JJ., Lopez, RR. 2007. Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary diferential equations. Acta Math. Sinica, Engl. Ser.,23(12): 2205-2212.
• Olatinwo, MO. 2008. On some common fixed point theorems of Aamri and El Moutawakil in uniform spaces. Applied Math. E-Notes,8: 254-262.
• Ran, ACM., Reurings, MCB. 2004. A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc.,132: 1435-1443.
• corollaries related to this fixed point and coupled fixed point theorems.
• Turkoglu, D., Binbasioglu, D. 2011. Some fixed point theorems for Multivalued Monotone Mappings in Ordered Uniform Space. Fixed Point Theo. Appl., Article ID:186237.
• Turkoglu, D., Binbasioglu, D. 2015. Coupled Coincidence point theorems for Compatible Mappings in Ordered Uniform Space. Miskolc Math. Not., 16(1): 527-541.
• Turkoglu, D. 2008. Some fixed point theorems for hybrid contractions in uniform space. Taiwanese J. Math.,12(3): 807- 820.