On Meir-Keeler type contraction via rational expression

Abstract

In this paper, we show that the continuity requirement assumed in the main result of Vara Prasad and Singh [Meir-Keeler type contraction via rational expression Acta Math. Univ. Comenianae Vol. LXXXIX, 1 (2020), 19-25] can be relaxed further. As a by-product we  explore some new answers to the open question posed by Rhoades [Contemporary Mathematics 72 (1988), 233-245] regarding the existence of contractive mappings that admit discontinuity at the fixed point.