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The concept of symmetry is a very vast topic that is involved in the studies of several phenomena. This concept enables us to discuss the phenomenon in some systematic pattern depending upon the type of phenomenon. Each phenomenon has its own type of symmetry. The phenomenon that is used in the discussion of this article is a symmetric distance-measuring function. This article presents the notions of abstract interpolative Reich-Rus-Ćirić-type contractions with a shrink map and examines the existence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-fixed points for such maps in complete metric space. These notions are defined through special types of simulation functions. The proof technique of the results presented in this article is easy to understand compared with the existing literature on interpolative Reich-Rus-Ćirić-type contractions.