Banach Contraction Principle in Cone Modular Spaces with Banach Algebra

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.

Anahtar Kelimeler:

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

Banach Cebirli Koni Modüler Uzaylarda Banach Büzülme Prensibi

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,

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