Banach Cebirli Koni Modüler Uzaylarda Banach Büzülme Prensibi

Year 2019, Volume: 19 Issue: 2, 335 - 342, 17.09.2019

Muttalip Özavşar Hatice Çay

Abstract

Bilinen anlamda büzülme
dönüşümü olmayan öyle dönüşümler vardır ki bu dönüşümler bazı yeni metrik ve
modüler uzay yapılarında bazı büzülme tipinde koşulları sağlarlar. Biz bu
makalede bu durumu göz önünde bulundurarak Banach cebirlerdeki konilerin
yardımıyla yeni bir modüler uzay kavramı sunduk. İlk kısımda temel tanım ve
notasyonlar verildi. İkinci kısımda Banach
Büzülme Prensibinin -cebir
değerli modüler uzaylardaki sonucuyla klasik modüler uzaylardaki sonucunun
denkliği gösterildi. Sonra yukarıda bahsedilen o modüler uzaya giriş yapıldı ve
bazı sonuçlar verildi. Son olarak çalışma bir örnekle desteklendi.

Keywords

Modüler uzay, Banach cebiri, sabit nokta teoremi, 〖 ∆ 〗_2-koşulu;, F-normu; C^*-cebiri

Banach Contraction Principle in Cone Modular Spaces with Banach Algebra

Abstract

There
are some mappings, which  are not
contraction mappings in the usual senses, such that they hold   some contractive type conditions in the
settings of some new abstract metric and modular spaces. In this paper, taking
into account this fact, we introduce such a new type modular space by using the
setting of cones in Banach algebras. In the first section, some basic notions
and definitions are given. In the second part, it is shown that some result of Banach
Contraction Principle in modular space with C^*-algebra is equivalent to the
result of Banach Contraction Principle of the usual modular space. Then that
new modular space mentioned above is introduced and some results are given.
Finally the work is concluded with an example.

Keywords

Modular Spaces, Banach Algebras, Fixed point theorem, 〖 ∆ 〗_2-condition, F-norm; C^*-algebra

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