Browsing by Author "Amubieya, Joseph Ayodele"

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    Existence of fixed points for a class of AΦ-contrcations in generalized metric space
    (Mathematics,Obafemi Awolowo University, 2016) Amubieya, Joseph Ayodele
    This study introduced a new and larger class of contraction mappings and determined conditions for existence and uniqueness of fixed points for the class of contraction mappings introduced. This is with a view to establishing the conditions for the existence and uniqueness of the fixed points for a class of AΦ−contractions in G−metric space and the method of their approximation. A contractive condition was defined. Some of existing ones in G−metric space was generalized. An iterative sequence was generated by the use of the defined contractions. The required conditions for the sequence to be Cauchy and convergent were obtained, and weak compatibility conditions were used in places where more than one operator were considered to approximate the common fixed points. The AΦ−contractions was found to be more general than Φ−contractions and larger than the A-contractions. Since generalized metric space was wider than the metric space, the corresponding results obtained extended those of the metric space. This study concluded that the existence of fixed points for this class of mappings was possible, if the generalized metric space was symmetric. Fixed points existed and unique for each of the contraction mappings.