| Summary: | Fixed point analysis is one of the most effective and valuable methods in modern mathematics,
and it can be considered a major subject of nonlinear analysis, which Banach
began in 1922. In this thesis, fundamental idea of fixed point analysis has been generalized
by expanding the domain of the contraction as a new contraction supported by a
weak triangular α-admissible mapping with regards to η and C−class function in the
class of partial b−metric spaces on a set W. For these novel contraction mappings, we
have proved the existence and uniqueness of the fixed point results. We have presented
an example and application as a result of our main theorems to establish the validity of
our fixed point results in the partial b−metric spaces to generalize and enhance various
studies in the literature.
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