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 AKHADKULOV^1*, 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

 

Received: 28 October 2016/Accepted: 23 January 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

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*Corresponding author; email: habibulla@uum.edu.my