Summary: | In this manuscript, some tripled fixed point results were derived under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>φ</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mo>ℓ</mo><mo>)</mo></mrow></semantics></math></inline-formula>-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory.
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