Karapınar, ErdalAgarwal, Ravi P.2025-09-052025-09-05202297816363918309781636390956978168173509297816817353379781636391106978163639080297816817386359781636390710978168173505497816817364191938-17431938-1751https://doi.org/10.1007/978-3-031-14969-6_1https://hdl.handle.net/20.500.12416/10344Fixed point theory can be described as a framework for researching and investigating the existence of the solution of the equation f(p) = p for a certain self-mapping f that is defined on a non-empty set X. As is expected, here, p is called the fixed point of the mapping f. On the other side, we may re-consider the fixed point equation f(p) = p as T(p) = f(p) - p= 0 and, accordingly, finding the zeros of the mapping T and finding the fixed point of f becomes an equivalent statement. This equivalence, not only enriches the fixed point theory but also, opens the doors to a wide range of potential applications in the setting of almost all quantitative sciences. For example, let us consider one of the classical open problems of number theory, finding perfect numbers: Let p be a self-mapping on a natural number such that p(n) is the sum of all divisors of n for n> 1. Thus, any fixed points of the function p give a perfect number. In particular, 6 is the smallest perfect numbers, and 2 74207280× (2 74207281- 1 ), with 44, 677, 235 digits, is the biggest known perfect number. © 2022 Elsevier B.V., All rights reserved.eninfo:eu-repo/semantics/closedAccessFixed Point ArithmeticNumber TheoryFixed Point EquationFixed Point TheoryFixed PointsNatural NumberNon-Empty SetsMappingBook Part10.1007/978-3-031-14969-6_12-s2.0-85143820812