Abstract

In this article, we introduce the notion of triple bipolar controlled metric space and prove some new fixed point theorems on this space, reformulate the concept of α-admissible mapping with respect to θ in triple bipolar controlled metric space, and introduce the concept of α-admissible crooked mapping with respect to θ in triple bipolar controlled metric space. We supported our results with suitable examples. We also present an application of the derived result to prove the existence and uniqueness solution of the cantilever beam problem, which is in fourth-order differential equation form.

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