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Starting from a weak concept of stability, introduced by Berinde [1] and called “weak stability”, in [27] we develop a weaker notion, named “w2-stability”. Therefore, in this paper we prove some results of this weaker stability concept for certain class of mappings and also we give some examples of w2-stable but not weak stable nor stable iterations. Because of the restriction of an “approximate” sequence, some fixed point iteration procedures are not weakly stable so if it is used a weaker type of sequence, the stability can be obtained in the meaning of a new concept. General Terms Fixed-point and coincidence theorems.

On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems