Some fixed point theorems in extended b-metric spaces

Banach contraction principle is one of the earlier and main results in fixed point theory. Banach contraction principle which guarantees existence and uniqueness of fixed point was proved in complete metric spaces in 1922 by Banach. According to this principle, ”let (X, d) be a complete metric space and f : X → X be a mapping. If there exists a constant 0 ≤ k < 1 such that for all x, y ∈ X, d( f x, f y) ≤ k.d(x, y), then f has a unique fixed point”. In this work, we define almost contraction in extended b-metric space and prove some fixed point theorems for mappings satisfying this type contraction.