Abstract
In this article we make an improvement in the Banach contraction using a controlled function in controlled metric like spaces, which generalizes many results in the literature. Moreover, we present an application on Fredholm type integral equation.
Highlights
One of the most interesting applications of fixed point theory is solving integral and differential equations; see, for example, [1]
We start by reminding the reader the definition of extended bmetric spaces
We propose a fixed point result using the nonlinear Kannantype contraction via the auxiliary function θ ∈ B
Summary
One of the most interesting applications of fixed point theory is solving integral and differential equations; see, for example, [1]. (X, dc) is called a controlled metric-type space. (X, dc) is called a controlled metric-like space. 0, which implies that (X, dc) is not a controlled metric-type space. Definition 1.5 ([25]) Let (X, dc) be a controlled metric-like space, and let {sn}n≥0 be a sequence in X.
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