In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric’s quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained without imposing a continuity condition on the mapping, thereby further generalizing some other related work in the literature. An example is given to show the validity of results obtained.
Very recently, Mogbademu [6] answered in affirmative the open problem proposed in [9] by extending an iterative algorithm for two asymptotically pseudocontractive mappings to three mappings. He further asked if his results could be extended to the case of finite family of mappings. This sequel gives a positive answer to the open problem and equally extends so many results in this area of research.
A strong convergence theorem for asymptotically generalized Φ− hemicontractive map in real Banach space is proved using the iterative sequence generated by this map. The result of this paper extend and improve the very recent result of Kim et al., (2009) which itself is a generalization of many of the previous results.
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