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In the present study, we prove generalizations of Banach, Kannan, Chatterjea, Čirič-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mapping contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by Bessenyei and Pâles. Such an approach allows us to derive corollaries for various types of semimetric spaces such as metric spaces, ultrametric spaces, and b-metric spaces. The significance of these generalized theorems extends across multiple disciplines, such as optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design. [ABSTRACT FROM AUTHOR]

Let X be a class of metric spaces and let Px be the set of all f: [0, oo) [0, oo) preserving X, i.e., (/, f o p) e X whenever (/, p) e X. For arbitrary subset A of the set of all metric preserving functions, we show that the equality Px = A has a solution if A is a monoid with respect to the operation of function composition. In particular, for the set SI of all amenable subadditive increasing functions, there is a class X of metric spaces such that Px = SI holds. 2020 Mathematics Subject Classification: Primary 26A30, Secondary 54E35, 20M20 [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalizations of the concept of MR-Kannan type contractions and utilize those conditions to derive new fixed point theorems under both contractive and non-contractive conditions. Our approach enhances various existing results related to enriched mappings. [ABSTRACT FROM AUTHOR]

In this note we point out errors in the proofs of first two theorems contained in Demonstratio Mathematica, Vol. XLVI, no 2, 2013, 405-413. We also rectify the erratic theorems by employing a proper setting.