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We consider diffusive motion of a particle performing a random walk withL\'evy distributed jump lengths and subject to resetting mechanism bringing thewalker to an initial position at uniformly distributed times. In the limit ofinfinite number of steps and for long times, the process converges to asuper-diffusive motion with replenishment. We derive formula for a mean firstarrival time (MFAT) to a predefined target position reached by a meanderingparticle and analyze efficiency of the proposed searching strategy byinvestigating criteria for an optimal (a shortest possible) MFAT.

Optimal first arrival times in L\'evy flights with resetting