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