Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701Solution and stability of a fixed point problem for mappings without continuity21092119661410.22075/ijnaa.2021.21698.2287ENBinayak SChoudhuryDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India0000-0002-7263-6636PriyamChakrabortyDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India0000-0001-5125-1465AmareshKunduDepartment of Mathematics, Chanchal College, Chanchal, Malda- 732123, West Bengal, IndiaJournal Article20201031In this paper by taking into account three trends prevalent in metric fixed point theory, namely, use of control functions instead of contraction constants, consideration of relational structure in the metric space and fixed point studies of discontinuous functions, we formulate and solve a new problem in relational metric fixed point theory. Our result extends the well known result of Kannan. The theorems are illustrated with examples. Further the proble is shown to have Hyers-Ulam-Rassias stability property. We make an application of our main result to a problem of a nonlinear integral equation.https://ijnaa.semnan.ac.ir/article_6614_90ed9bf0c1abeaadf3f230f4d1ead2ae.pdf