Vatan Karakaya - Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, ۳۴۲۱۰ Istanbul, Turkey.
Necip Şimşek - Department of Mathematics, Istanbul Commerce University, Sutluce Campus, Beyoglu, ۳۴۴۴۵ Istanbul, Turkey.
Derya Sekman - Department of Mathematics, Ahi Evran University, Bagbasi Campus, ۴۰۱۰۰ Kirsehir, Turkey.

The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the other important classes. Along with that, α-admissible mapping is a different approach in the fixed point theory. According to this method, a single or multivalued mapping does not have a fixed point in general. But, under some restriction on the mapping, a fixed point can be obtained. In this article, we combine four significant notions and also establish fixed point theorem for this mappings in complete metric spaces. Moreover, we give an example to show the interesting of our results according to earlier results in literature.

Fixed point theory, $alpha $-admissible mappings, Multivalued integral operators, $F$-weak contraction