The Journal of the Indian Mathematical Society

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On Discontinuity and Fixed Points


Affiliations
1 Depaitment of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263 002, India
2 Department of Mathematics, Kathmandu University, P.O. Box No. 1250, Kathmandu, Nepal
     

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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].
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  • On Discontinuity and Fixed Points

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Authors

Vyomesh Pant
Depaitment of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263 002, India
K. Jha
Department of Mathematics, Kathmandu University, P.O. Box No. 1250, Kathmandu, Nepal

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].