Abstract
In this paper, we introduce a new contraction via CF -simulation function and prove the existence and the uniqueness of our mapping defined on a metric-like space. Our work generalizes and extends some theorems in the literature. An example and application of second type of Fredholm integral equation are given.
Highlights
We introduce a new contraction via CF -simulation function and prove the existence and the uniqueness of our mapping defined on a metric-like space
Many problems in mathematics and other sciences such as physics, chemistry, computer science and engineering resolved by using fixed point theory
One of the most spaces introduced in this decade is metric-like space that was presented by Amini-Harandi [11] in 2012
Summary
Many problems in mathematics and other sciences such as physics, chemistry, computer science and engineering resolved by using fixed point theory. A lot of researchers proved (common) fixed point results by using different types of contractive conditions in the setting of metric-like spaces, for example see( [2], [3], [6]- [10]). An extended CF -simulation function, fixed point, metric-like spaces. [25] A mapping ζ : R+ × R+ → R an extended CF -simulation function if satisfying the following conditions: (ζ1) ζ(α, ξ) < F (α, ξ), where α, ξ > 0, with property CF (ζ2) if {αn}, {ξn} are sequences in (0, ∞) such that lim n→∞. In this article, motivated by the idea of an extended CF -simulation function due to Chanda et al 1.3, we prove the existence and the uniqueness of a common fixed point for two mappings satisfying a contraction which involve a lower semicontinuous function is established. An example and application are given to support the obtained work
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