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 equal 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.

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 equal 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.