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In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+\overline{f_2(z)}$ under the integral operator  $I_{f}(z)=\int_{0}^{z}\frac{f_1(u)}{u}du+\overline{\int_{0}^z\frac{f_2(u)}{u}}$ and obtain the sharp constant $\frac{4\sqrt{6}-\sqrt{15}}{9}$, which generalized the result corresponding to the class of analytic functions given by Nash.

SHARP HEREDITARY CONVEX RADIUS OF CONVEX HARMONIC MAPPINGS UNDER AN INTEGRAL OPERATOR