Sains Malaysiana 46(8)(2017): 1341–1346

http://dx.doi.org/10.17576/jsm-2017-4608-21

 

The Existence of ϒ-fixed Point for the Multidimensional Nonlinear Mappings Satisfying (ψ, θ, ϕ)-weak Contractive Conditions

(Kewujudan Titik ϒ-tetap pada Pemetaan Tak-linear Multidimensi yang Ditakrifkan Terhadap Ruang Metrik Bertertib Separa dan Memenuhi Syarat Penguncupan

(ψ, θ, ϕ)-lemah)

 

HABIBULLA AKHADKULOV1*, RAHMA ZUHRA2, AZIZAN BIN SAABAN1, FAWZIA SHADDAD3 & SOKHOBIDDIN AKHATKULOV2

 

1School of Quantitative Sciences, Universiti Utara Malaysia, CAS 06010, UUM Sintok, Kedah Darul Aman, Malaysia

 

2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

3Department of Mathematics, Sana'a University, Yemen

 

Diserahkan: 28 Oktober 2016/Diterima: 23 Januari 2017

 

 

ABSTRACT

In this paper we prove the existence of ϒ-fixed point for a multidimensional nonlinear mappings F : Xk X defined on the partially ordered metric spaces and satisfying (ψ, θ, ϕ)-weak contractive conditions. Moreover, we prove the uniqueness of that fixed point under extra conditions to (ψ, θ, ϕ)-weak contractive conditions.

 

Keywords: Contractive condition; fixed-point; partially ordered metric space

 

ABSTRAK

Dalam kertas ini, kami buktikan kewujudan titikϒ-tetap pada pemetaan tak-linear multidimensi F : Xk X yang ditakrifkan terhadap ruang metrik bertertib separa dan memenuhi syarat penguncupan (ψ, θ, ϕ)-lemah. Seterusnya, kami buktikan keunikan titik tetap tersebut dengan syarat tambahan kepada syarat (ψ, θ, ϕ)-lemah.

 

Kata kunci: Ruang metrik bertertib separa; syarat pengucupan; titik tetap

RUJUKAN

Aydi, H., Karapinar, E. & Postolache, K. 2012. Tripled coincidence point theorems for weak j-contractions in partially ordered metric spaces. Fix. Point Theo. Appl. 1: 1-12.

Banach, S. 1922. Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fund. Math.3: 133-181.

Berinde, V. & Borcut, M. 2011. Tripled fixed point theorems for contractive type mappings in partially ordered matric space. Non Anal. Theo, Meth. & Appl. 74: 4889-4897.

Bhaskar, G. & Lakshmikantham, V. 2006. Fixed point theorems in partially ordered metric space and applications. NonL. Anal. Theo, Meth. & Appl. 65(7): 1379-1393.

Choudhury, B. 2012. (y;a;b)-weak contractions in partially ordered metric spaces. Appl. Math. Lett.25(1): 6-10.

Guo, J. & Lakshmikantham, V. 1987. Coupled fixed points of nonlinear operators with applications. NonL. Anal. Theo, Meth. & Appl. 11(5): 623-632.

Karapinar, E. 2011. Quadruple fixed point theorems for weak f-contractions. ISRN Math. Anal.2011: Article ID. 989423.

Khan, S., Swaleh, M. & Sessa, S. 1984. Fixed point theorems by altering distances between the points. Bull. Aus. Math. Soc. 30(1): 1-9.

Rold´an, A., Mart´ınez-Moreno, J. & Rold´an, C. 2012. Multidimensional fixed point theorems in partially ordered complete metric spaces. J. Math. Anal. Appl. 396(2): 536-545.

Shaddad, F., Noorani, M., Alsulami, M. & Akhadkulov, H. 2014. Coupled point results in partially ordered metric spaces without compatibility. Fix. Point Theo. Appl. 2014: 204.

 

 

*Pengarang untuk surat-menyurat; email: habibulla@uum.edu.my

 

 

 

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