Buescu, Jorge; Serpa, Cristina Compatibility conditions for systems of iterative functional equations with non-trivial contact sets. (English) Zbl 1469.39010 Result. Math. 76, No. 2, Paper No. 68, 19 p. (2021). Summary: Systems of iterative functional equations with a non-trivial set of contact points are not necessarily solvable, as the resulting intersections may lead to an overdetermination of the system. To obtain existence and uniqueness results additional conditions must be imposed on the system. These are the compatibility conditions, which we define and study in a general setting. An application to the affine and doubly affine cases allows us to solve an open problem in the theory of functional equations. In the last section we consider a special problem in a different perspective, showing that a complex compatibility condition may result in an elegant and simple property of the solution. MSC: 39B12 Iteration theory, iterative and composite equations 39B72 Systems of functional equations and inequalities Keywords:compatibility condition; system of iterative functional equations; fractal interpolation; contact point; contact set PDFBibTeX XMLCite \textit{J. Buescu} and \textit{C. Serpa}, Result. Math. 76, No. 2, Paper No. 68, 19 p. (2021; Zbl 1469.39010) Full Text: DOI References: [1] Xu, P., A discussion on fractal models for transport physics of porous media, Fractals, 23, 3, 1530001 (2015) [2] Mambetsariev, I.; Mirzapoiazova, T.; Lennon, F.; Jolly, MK; Li, H.; Nasser, MW; Vora, L.; Kulkarni, P.; Batra, SK; Salgia, R., Small cell lung cancer therapeutic responses through fractal measurements: from radiology to mitochondrial biology, J. Clin. Med., 8, 7, 1038 (2019) [3] Uahabi, KL; Atounti, M., Applications of fractals in medicine, An. Univ. Craiova Ser. Mat. Inform., 42, 1, 167-174 (2015) · Zbl 1363.92016 [4] Takayasu, M.; Takayasu, H.; Meyers, R., Fractals and economics, Complex Systems in Finance and Econometrics (2009), New York: Springer, New York · Zbl 1175.91131 [5] Barnsley, M., Fractal functions and interpolation, Constr. Approx., 2, 303-329 (1986) · Zbl 0606.41005 [6] Kim, JM; Kim, HJ; Mun, HM, Nonlinear fractal interpolation curves with function vertical scaling factors, Indian J. Pure Appl. Math., 51, 2, 483-499 (2020) · Zbl 1450.37021 [7] Serpa, C.; Buescu, J., Explicitly defined fractal interpolation functions with variable parameters, Chaos Solitons Fractals, 75, 76-83 (2015) · Zbl 1352.41001 [8] Wang, H-Y; Yu, J-S, Fractal interpolation functions with variable parameters and their analytical properties, J. Approx. Theory, 175, 1-18 (2013) · Zbl 1303.28014 [9] Liu, J., Shi, Y.-G.: Conjugacy problem of strictly monotone maps with only one jump discontinuity. Results Math. 75, 90 (2020) · Zbl 1440.37033 [10] Serpa, C.; Buescu, J., Non-uniqueness and exotic solutions of conjugacy equations, J. Differ. Equ. Appl., 21, 12, 1147-1162 (2015) · Zbl 1344.39011 [11] Serpa, C.; Buescu, J., Constructive solutions for systems of iterative functional equations, Constr. Approx., 45, 273-299 (2017) · Zbl 1369.39019 [12] Buescu, J.; Serpa, C., Fractal and Hausdorff dimensions for systems of iterative functional equations, J. Math. Anal. Appl., 480, 123429 (2019) · Zbl 1426.28015 [13] Okamura, K., Some results for conjugate equations, Aequationes Math., 93, 1051-1084 (2019) · Zbl 1429.39020 [14] Massopust, PR, Fractal functions and their applications, Chaos Solitons Fractals, 8, 2, 171-190 (1997) · Zbl 0919.58035 [15] Zeitler, H., Affine mappings in iterated function systems, Result Math., 46, 181-194 (2004) · Zbl 1056.28007 [16] Ioana, L.; Mihail, A., Iterated function systems consisting of \(\varphi \)-contractions, Results Math., 72, 2203-2225 (2017) · Zbl 1381.28010 [17] Massopust, PR, On some generalizations of B-splines, Monografias Matemáticas Garcia de Galdeano, 42, 203-217 (2019) [18] De Rham, G.: Sur quelques courbes definies par des equations fonctionnelles. Univ. e Politec. Torino, Rend. Sem. Mat. 16, 101-113 (1957) · Zbl 0079.16105 [19] Mayor, G.; De Torrens, J., De Rham systems and the solution of a class of functional equations, Aequationes Math., 47, 43-49 (1994) · Zbl 0802.39008 [20] Girgensohn, R., Functional equations and nowhere differentiable functions, Aequationes Math., 46, 243-56 (1993) · Zbl 0788.26007 [21] Matkowski, J.: Integrable solutions of functional equations. Dissertationes Math. (Rozprawy Mat.) 127 (1975) · Zbl 0318.39005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.