Abstract
We will first introduce the fixed point property and a new class of operators and contraction mapping for classes of ϕ-contractions in E−G-metric spaces. Also, we will realize the study of the fixed point theory for (local and global) nonlinear contractions with an o-comparison function in E −G-metric spaces. We also introduce Gopen ball, G-closed ball and X(x0,r) and obtain some fixed point theorems. Furthermore we give an application to a Fredholm-Volterra type differential equation where one of the integral operators satisfies ϕ-contraction condition.
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