Article

ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 57, Issue 1, pp 181-190

Weak reciprocal continuity and fixed point theorems

  • R. P. PantAffiliated withDepartment of Mathematics, Kumaun University Nainital
  • , R. K. BishtAffiliated withDepartment of Mathematics, Kumaun University Nainital Email author 
  • , D. AroraAffiliated withDepartment of Mathematics, Kumaun University Nainital

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Abstract

The aim of the present paper is to introduce the notion of weak reciprocal continuity and obtain fixed point theorems by employing the new notion. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. Our results generalize several fixed point theorems.

Keywords

Fixed point theorems Nonexpansive mapping Compatible maps Noncompatible maps R-weakly commuting mappings Reciprocal continuity R-weakly commuting of type (Af ) and of type (Ag )

Mathematics Subject Classification (2000)

47H09 47H10 54H25