**4. Conclusions**

In this paper, we combine and extend significant fixed-point results, namely Suzuki [2], Popescu [1], and Pata [4] by involving the admissible mappings. As in [3] (see also [19]), by proper choice of the auxiliary admissible mapping *α* and replacing the set *<sup>P</sup>*(<sup>κ</sup>, *y*) with some concrete subset, we can derive several more consequences. Since the techniques are the same in [3], we skip the details and we avoid listing all possible corollaries. Indeed, Theorem 4 and Theorem 5 are the basic examples of this consideration. Notice also that the given example and an integral equation can be improved according to choice of *α*.

**Author Contributions:** O.A. analyzed and prepared the manuscript, V.M.L. H.B. analyzed and prepared/edited the manuscript, E.K. analyzed and prepared/edited the manuscript, All authors read and approved the final manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors are grateful to the handling editor and reviewers for their careful reviews and useful comments. The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this group No. RG-1440-025.

**Conflicts of Interest:** The authors declare no conflict of interest.
