Fixed points of mappings satisfying some contractive condition in modular spaces

In the first part of this study which is prepared as six sections, some basic definitions and theorems which will be used in later sections were given. In the second chapter, a functional which is called modular has been investigated. The modular space structure defined by the modular as studied. In these spaces, some topological properties and concepts related to fixed point theory were given. At the end of this section, modular spaces equipped with a graph were examined. In the third chapter, some fixed and common fixed point theorems are proved in modular spaces for weakly compatible mappings that provide generalized almost contractive conditions including comparison functions. In the fourth chapter, some fixed point results were obtained in modular spaces by defining the generalized almost -contractive condition. In addition, connected and -graph concepts were introduced and common fixed point theorems were given for two mappings. In the fifth chapter fixed point theorems related to the existence and uniqueness of the common fixed points of generalized almost -contraction mappings obtained by using the comparison function class and A-class contraction mappings on the modular space were studied. Also, some results have been obtained for mappings which involve the integral type contractive condition. In the last section, B_φ^f-contraction mappings and integral type contraction mappings are defined, By using these mappings, the existence and uniqueness of the fixed point of pairs on the modular space have been proved and some results have been obtained.