As main result we prove that Fejér means of Walsh–Kaczmarz–Fourier series are uniformly bounded operators from the Hardy martingale space $$\ H_{p}$$ to $$H_{p}$$ for $$ 0<p\le 1/2$$ .

In this paper we introduce strong $I^K$-convergence of functions which is common generalization $I^*$-convergence in probabilistic metric spaces. We also define and study $I^{K}$-limit points same space.