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

We introduce in this paper some concepts of <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-admissible triangular mappings with respect to a function <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> and the concept of <inline-formula> <tex-math notation="LaTeX">$(\alpha ,\beta ,\psi )$ </tex-math></inline-formula>-contraction. We also utilize our new concept to prove a fixed point theorem based on the contractive condition of type <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-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.

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