The Journal of the Indian Mathematical Society

R. P. Pant ¹, K. Jha ², A. B. Lohani ¹

Affiliations
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, Uttaranchal, IN
2 Department of Mathematical Sciences, Kathmandu University, P.O. Box-6250, Kathmandu, NP

Abstract

The aim of the present paper is to obtain a fixed point theorem for a sequence of mappings satisfying a weak form of Meir-Keeler type (ε,δ)- contractive condition together with a (Φ-contractive condition without assuming any additional conditions on δ and Φ. The present theorem extends and unifies the Meir-Keeler type and a Φ-contractive type fixed point theorems.

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Vyomesh Pant ¹, K. Jha ²

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

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].

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