Sufficient Conditions for a Real-Valued Function to have a Unique Root or No Root at All

Daniel Solow () and Qi Wu ()
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Daniel Solow: Case Western Reserve University
Qi Wu: Case Western Reserve University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 2, No 6, 12 pages

Abstract: Abstract In this work, a new sufficient condition for the existence of a unique root of a continuously differentiable real-valued function of one variable is presented. Conditions are also given under which one can conclude that the function has no root. Specific applications in financial planning and operations management are shown to satisfy these sufficient conditions. These results also have implications for the line-search problem, which is used in most algorithms for solving differentiable nonlinear optimization problems.

Keywords: Roots of functions; Existence and uniqueness of roots; Real-valued functions; Line-search problem (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02587-z

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