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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).

Well-posedness of fixed point problem for mappings satisfying an implicit relation

Akkouchi M., Popa V.

Demonstratio Mathematica

2010

Vol. 43, nr 4

923-929

The notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.