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This article reports the results of experiments aimed at producing hypothetical long-lived superheavy elements located near the spherical-shell closures with Z ≥ 114 and N ≥ 172. For the synthesis of superheavy nuclei, we used a combination of neutron-rich reaction partners, with a [sup 244]Pu target and a [sup 48]Ca projectile. The sensitivity of the present experiment exceeded by more than two orders of magnitude previous attempts at synthesizing superheavy nuclides in reactions of [sup 48]Ca projectiles with actinide targets. We observed new decay sequences of genetically linked alpha decays terminated by spontaneous fission. The high measured alpha-particle energies, together with the long decay times and spontaneous fission terminating the chains, offer evidence for the decay of nuclei with high atomic numbers. The decay properties of the synthesized nuclei are consistent with the consecutive alpha decays originating from the parent nuclides [sup 288, 289]114, produced in the 3n- and 4n-evaporation channels with cross sections of about a picobarn. The present observations can be considered experimental evidence for the existence of the "island of stability" of superheavy elements and are discussed in terms of modem theoretical approaches. [ABSTRACT FROM AUTHOR]