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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.

Common fixed points of conditionally commuting mappings satisfying weaker continuity conditions

Bisht R K

Fasciculi Mathematici

2012

Nr 49

33--41

The aim of the present paper is to obtain some new common fixed point theorems for a pair of Lipschitzian type selfmappings satisfying a minimal commutativity and weaker continuity conditions. In the setting of our results we establish a situation in which a pair of mappings may possess common fixed points as well as coincidence points which may not be common fixed points. Our results generalize several fixed point theorems.