The complement on the existence of fixed points that belong to the zero set of a certain function due to Karapinar et al

Abstract

Recently, the idea of ϕ-fixed point and the elementary results on ϕfixed points were first investigated by Jleli et al. [Jleli M, Samet B, Vetro C (2014) Fixed point theory in partial metric spaces via ϕ-fixed point’s concept in metric spaces. Journal of Inequalities and Applications, 2014(1):1-9.]. Based on this work, Karapinar et al. [Karapinar E, O’Regan D, Samet B (2015) On the existence of fixed points that belong to the zero set of a certain function. Fixed Point Theory and Applications, 2015(1):1-14.] established the new ϕ-fixed point results, which can be reduced to the famous fixed point result of Boyd and Wong in 1969. However, the main result of Karapinar et al. does not cover the ϕ-fixed point results of Jleli et al. This paper aims to fulfill this gap by proving ϕ-fixed point results covering several ϕ-fixed point results and fixed point results.