*Correspondence: [email protected] 1Young Researcher and Elite Club, Arak-Branch, Islamic Azad University, Arak, Iran Full list of author information is available at the end of the article Abstract In this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce th...