University of MaraghehSahand Communications in Mathematical Analysis2322-580720220230301On Fixed Points of a General Class of Hybrid Contractions with Ulam-Type Stability396470098710.22130/scma.2022.551742.1093ENJamilu AbubakarJiddahDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.MohammedShehu ShagariDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.0000-0002-0365-2878Abdussamad TankoImamDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.Journal Article20220411In this paper, a new general class of contraction, namely admissible hybrid $(G$-$\alpha$-$\phi)$-contraction is introduced and some fixed point theorems that cannot be deduced from their corresponding ones in metric spaces are proved. The distinction of this family of contractions is that its contractive inequality can be specialized in several ways, depending on multiple parameters. Consequently, several corollaries, including some recently announced results in the literature are highlighted and analyzed. Nontrivial comparative examples are constructed to validate the assumptions of our obtained theorems. We further examine Ulam-type stability and well-posedness for the new contraction proposed herein. In addition, one of our obtained corollaries is applied to set up novel existence conditions for the solution of a class of integral equations. There is an open problem concerning the discretized population balance model, whose solution may be analyzed using the methods established here.https://scma.maragheh.ac.ir/article_700987_025526d746fb20abca6e56a394c07d0a.pdf