Abstract
A Common Fixed Point Theorem for Self Maps on a Metric Space using Pseudo Altering Distance Function and a Deficit Function
Highlights
THE study of fixed points of mappings satisfying certain conditions has been at the centre of rigorous research activity
We introduce the notion of a pseudo altering distance function and obtain a common fixed point theorem
In the results of earlier authors, dealing with generalized contractions involving an altering distance function ψ and a deficit function φ no link is given between ψ and φ
Summary
THE study of fixed points of mappings satisfying certain conditions has been at the centre of rigorous research activity. Gairola & Ram Krishan (2013) presented fixed point results for three self maps satisfying a generalized weak contraction condition by using the concept of weakly compatible maps in a complete metric space. These results extend and generalized the results of Choudhary et al, (2011). A generalized weak contraction condition involves an altering distance function which is increasing and continuous. We introduce the notion of a pseudo altering distance function (doing away with continuity) and obtain a common fixed point theorem. In the results of earlier authors, dealing with generalized contractions involving an altering distance function ψ and a deficit function φ no link is given between ψ and φ. Function φ, we prove a common fixed point theorem which extends the results of Gairola & Ram Krishan (2013)
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