Generalized perturbed contractions with related fixed point results

In this paper, we introduce the concept of -perturbed contraction in a metric space and we establish some fixed point theorems which extends the results from Branga, A. N. Olaru, I. M. Some Fixed Point Results in Spaces with Perturbed Metrics. Carpathian J. Math.  38 (2022), no. 3, 641–654 and Olaru, I. M.; Secelean, N. A. A new approach of some contractive mappings on metric spaces.  Mathematics 9 (2021), 1433. Also, an application to an integral equation and some illustrative examples are given throughout the paper.