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A generalized common fixed point theorem under an implicit relation

Surekha D., Phaneendra T.

Demonstratio Mathematica

2015

Vol. 48, nr 1

91--99

An extended generalization of recent result of Kikina and Kikina (2011) has been established through the notions of weak compatibility and the property E.A., under an implicit-type relation and restricted orbital completeness of the space. The result of this paper also extends and generalizes that of Imdad and Ali (2007).

Two generalized common fixed point theorems involving compatibility and property E.A.

Phaneendra T., Prasad V. S. R.

Demonstratio Mathematica

2014

Vol. 47, nr 2

449--458

We prove two generalizations: the first to Das and Naik’s theorem for a pair of compatible maps without continuity; and the next as an extension of our first result to three self-maps on a metric space X without compatibility, under a stronger contraction type inequality and restricting the completeness of X to its subspace. The latter is a significant generalization of a recent result of Pant et al.