In this paper, we have some observations on F-weak contractions due to Wardowski and Van Dung (Demonstr Math 47(1):146–155, 2014). Our observations lead us to introduce the notion of \(F^*\)-weak contractions and utilize the same to prove some fixed point results. The proven results give an affirmative answer to certain open questions raised by Kannan (Bull Calcutta Math Soc 60:71–76, 1968) and Rhoades (Contemp. Math. 72:233–245, 1988) on the existence of contractive definitions not forcing the continuity at the fixed point. Some illustrative examples are also given. As an application, we investigate the existence and uniqueness of the solution of an integral equation of Volterra type.

中文翻译：

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关于F弱收缩和不连续点的观察及其应用

在本文中，我们对由Wardowski和Van Dung引起的F弱收缩进行了观察（Demonstr Math 47（1）：146–155，2014）。我们的观察使我们引入了\（F ^ * \）-弱收缩的概念，并利用它来证明一些不动点结果。经验证的结果对Kannan（Bull Calcutta Math Soc 60：71–76，1968）和Rhoades（Contemp。Math。72：233–245，1988）提出的某些未解决的强制性问题给出了肯定的回答。在固定点的连续性。还给出了一些说明性的例子。作为一种应用，我们研究了Volterra型积分方程解的存在性和唯一性。