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

 

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

 

 

 

 

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