On Discontinuity and Fixed Points

Abstract

The present paper is aimed at proving a fixed point theorem under the (ε,δ) contractive condition, however without either imposing any additional restriction on δ or on the continuity of the map or assuming the Φ-contractive condition together with it. In the setting of the fixed point theorem we show that the map is discontinuous at the fixed point. Our theorem extends the results of Pant [Theorem 1, [13]] and Pant [17].