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Abstract <p>The results related to the basic concepts in mathematics (principles) were established mostly before the 20th century and have arisen very rarely since then. One similar principle was obtained quite recently for the real functions of one variable. It gives upper bounds for the number of zeros for the ‘‘enough smooth’’ functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f(t)\)</EquationSource> <!--LobJMat2560981Barsegian-m1--> </InlineEquation>. Commenting on this result some well-known mathematicians noticed that this principle plays for real function a role similar to that of the argument principle for analytic functions. In this paper, we give a new version of the principle which indeed is very similar to the argument principle. The number of zeros of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f(t)\)</EquationSource> <!--LobJMat2560981Barsegian-m2--> </InlineEquation> is estimated in terms of some angles like in the argument principle.</p>

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A New Principle in Real Analysis (Analogous to the Argument Principle in Complex Analysis)

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • G. Barsegian

摘要

Abstract

The results related to the basic concepts in mathematics (principles) were established mostly before the 20th century and have arisen very rarely since then. One similar principle was obtained quite recently for the real functions of one variable. It gives upper bounds for the number of zeros for the ‘‘enough smooth’’ functions \(f(t)\) . Commenting on this result some well-known mathematicians noticed that this principle plays for real function a role similar to that of the argument principle for analytic functions. In this paper, we give a new version of the principle which indeed is very similar to the argument principle. The number of zeros of \(f(t)\) is estimated in terms of some angles like in the argument principle.