Fixed point theorems for $$\alpha $$ α -integral type G-contraction mappings

In this paper, we introduce the notion of $$\alpha $$ α -integral type G-contraction mappings to generalize the notions of Banach G-contraction and integral G-contraction mappings. We also prove some fixed point theorems for $$\alpha $$ α -integral type G-contraction mappings. By providing some example, we show that our results are real generalization of several results in literature.