Kumar, Sunil; Shukla, D. P. Lipschitz type mappings in metric spaces with fixed points and maximum fixed points of magic squares. (English) Zbl 1259.54022 J. Indian Acad. Math. 31, No. 2, 491-501 (2009). Lipschitz type compatible pairs of mappings are considered by employing generalized Meir-Keeler type conditions to obtain fixed points. As an application, a method for construction of magic squares of various orders like \(4n \times 4n\), \((4n + 2) \times (4n + 2)\) with a view of obtaining maximum fixed points is proposed. It is claimed that the maximum number of possible fixed points of a \(4n \times 4n\) magic square is half of the total number of elements of the magic square. Prior to some simple remarks, the work ends with a plan to attempt a proof in some later paper of a hypothesis that the maximum number of possible fixed points of \((8n - 2) \times (8n - 2)\) magic square is equal to \((8n - 2)(8n - 3)/2\) whenever \((8n - 2)/2\) is a prime number and that the maximum number of possible fixed points of \((8n + 2) \times (8n + 2)\) magic square is equal to \((8n + 2)(8n + 1)/2 - 2\), if \((8n + 2)/2\) is a prime number. Reviewer: Neeraj Anant Pande (Nanded) MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 54E40 Special maps on metric spaces 05B15 Orthogonal arrays, Latin squares, Room squares Keywords:compatible mappings; fixed points; Lipschitz type mappings; magic squares PDFBibTeX XMLCite \textit{S. Kumar} and \textit{D. P. Shukla}, J. Indian Acad. Math. 31, No. 2, 491--501 (2009; Zbl 1259.54022)