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We introduce in this paper some concepts of    $alpha $   -admissible triangular mappings with respect to a function    $beta $    and the concept of    $(alpha ,beta ,psi )$   -contraction. We also utilize our new concept to prove a fixed point theorem based on the contractive condition of type    $alpha $   -admissibility. We apply our main result to derive many fixed point results. Also, we construct some examples to support our work. In the literature, many exciting results are improved and extended using our results.

Fixed Point Results for Mapping of Nonlinear Contractive Conditions of $\alpha$ -Admissibility Form