TY  - JOUR
T1  - New fixed-disc results via bilateral type contractions on S-metric spaces
TT  - S-metrik uzaylarda ikili tipinde daralmalar yardımıyla yeni sabit-disk sonuçları
AU  - Taş, Nihal
PY  - 2022
DA  - January
DO  - 10.25092/baunfbed.995307
JF  - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - BAUN Fen. Bil. Enst. Dergisi
PB  - Balıkesir University
WT  - DergiPark
SN  - 1301-7985
SP  - 408
EP  - 416
VL  - 24
IS  - 1
LA  - en
AB  - There are some examples of self-mappings which does not satisfy the Banach contractive condition and have a unique fixed point or more than one fixed point.  In this case, metric fixed-point theory has been extensively generalized using some techniques.  One of these techniques is to generalize the used contractive conditions such as the Jaggi type contractive condition, the Dass-Gupta type contractive condition etc.  Another technique is to generalize the used metric spaces such as a b-metric space, an S-metric space etc.  The last technique is to investigate geometric properties of the fixed-point set of a given self-mapping such as fixed circle, fixed disc etc.  For this purpose, “fixed-circle problem” has been studied with various techniques as a geometrical generalization of the metric fixed-point theory.  This problem was also considered as “fixed-figure problem”.  Some solutions to these recent problems were obtained using different contractions both a metric space and a generalized metric space.  The main purpose of this paper is to prove some fixed-disc theorems on an S-metric space.  To do this, we modify the known contractive conditions.  Also, the obtained new theorems are supported by some illustrative examples.
KW  - Fixed disc
KW  - fixed circle
KW  - bilateral type contraction
KW  - S-metric space
KW  - fixed-circle problem
N2  - Banach daralma koşulunu sağlamayan ve bir tek sabit noktası ya da birden fazla sabit noktası olan fonksiyon örnekleri mevcuttur.  Bu durumda, metrik sabit-nokta teorisi bazı teknikler kullanılarak kapsamlı olarak genelleştirilmektedir. Bu tekniklerden biri Jaggi tipinde daralma koşulu, Dass-Gupta tipinde daralma koşulu gibi kullanılan daralma koşulunun genelleştirilmesidir.  Diğer bir teknik ise b-metrik uzay, S-metrik uzay gibi kullanılan metrik uzayın genelleştirilmesidir.  Son teknik ise sabit çember, sabit disk gibi verilen bir fonksiyonun sabit nokta kümesinin geometrik özelliklerinin incelenmesidir.  Bu amaç için, “sabit-çember problemi” metrik sabit-nokta teorisinin geometrik bir genellemesi olarak çeşitli tekniklerle çalışılmaktadır.  Bu problem ayrıca “sabit-figür problemi” olarak da düşünülebilir.  Bu son problemlere bazı çözümler hem metrik uzaylar üzerinde hem de genelleştirilmiş metrik uzaylar üzerinde farklı daralmalar kullanılarak elde edilmiştir.  Bu makalenin ana amacı S-metrik uzaylar üzerinde bazı sabit-disk teoremleri ispatlamaktır.  Bunun için, Bunun için bilinen bazı daralma koşullarını modifiye edeceğiz.  Ayrıca elde edilen bu yeni teoremleri bazı gerçekleyici örnekler ile destekleyeceğiz.
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UR  - https://doi.org/10.25092/baunfbed.995307
L1  - https://dergipark.org.tr/en/download/article-file/1973934
ER  -