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Well-posedness and common fixed points for two pairs of maps using weak contractivity

Akkouchi M.

Demonstratio Mathematica

2013

Vol. 46, nr 2

373--382

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized ϕ-weak contraction, Appl. Math. Lett. 22(2009), 75-78] and [D. Dorić, Common fixed point for generalized (...)-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900] to prove a common fixed point theorem for four mappings satisfying generalized weak contractive condition (see Filomat 24:2 (2010), 1–10). In this paper, we generalize this theorem by using the concept of common property (E.A). Our result generalizes and unifies several existing results involving generalized weak contractive conditions. We study also well-posedness of a related fixed point problem.

The convergence of Jungck-type iterative schemes for generalized contractive-like operators

Olaleru J. O., Akewe H.

Fasciculi Mathematici

2010

Nr 45

87-98

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like opera- tors defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa and Jungck-Noor itera- tions can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations and extensions of the work of Olatinwo and Imoru [13], Olatinwo [14-15]. Consequently, several results in literature are generalized.

Existence conditions in symmetric multivalued vector quasiequilibrium problems

Anh L. Q., Khanh P. Q.

Control and Cybernetics

2007

Vol. 36, no 3

519-530

We consider symmetric multivalued vector quasiequilibrium problems in topological vector spaces. Sufficient conditions for the solution existence are established under relaxed assumptions, which are shown by examples to be essential, easy to check and more advantageous than recent known results. Applications to lower and upper bounded quasiequilibrium problems and to coincidence point problems are given.