| Summary: | In this paper, we will introduce a new geometric constant <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Also, this new coefficient is computed for <i>X</i> being concrete space.
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