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The intent of this paper is to prove the relation-theoretic fixed point results under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-contractions involving <i>W</i>-distance on a metric space and equipped with a symmetric locally <i>T</i>-transitive binary relation (not necessarily transitive relation). Our results enrich and improve several fixed point results of the existing literature.