Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations

Ulam type stability problems for alternative homomorphisms

We introduce an alternative homomorphism with respect to binary operations and investigate the Ulam type stability problem for such a mapping. The obtained results apply to Ulam type stability problems for several important functional equations.ArticleJOURNAL OF INEQUALITIES AND APPLICATIONS. 2014:228 (2014)journal articl

Anti-pathogenic properties of plant peptide hormone phytosulfokines [PSK's] and its selected analogues

Phytosulfokine-α (PSK-α) (H-Tyr(SO3H)-Ile-Tyr(SO3H)-Thr-Gln- OH) (I), a sulfated growth factor universally found in both monocotyledons and dicotyledons, strongly promotes proliferation of plant cells in culture. The C-terminal truncated analog named PSK-β (Tyr(SO3H)-Ile-Tyr(SO3H)-Thr) (II) showed a 10-fold lower activity than that of the parent pentapeptide. Because PSK-α promotes proliferation and differentiation during the plant growth we undertook the studies on the influence of PSK-α on plant defense mechanisms in that period. In present studies on PSK-α (I), PSK-β (II), and its analogues, we performed a search of another biological properties. The aim of our investigation was evaluation of PSK-α, PSK-β and their selected analogues in relation to growth and development of plant pathogens, such as Phoma narcissi and Botrytis tulipae. In these studies we elaborated the synthesis of PSK-α or PSK-β and their 22 analogues modified by natural and non-natural amino acid residues. Peptides were synthesized by the solid phase method according to the Fmoc procedure on a Wang-resin. Free peptides were released from the resin by 95% TFA in the presence of EDT. Biological effect of these peptides was evaluated by test on the growth and development of pathogens of P. narcissi and B. tulipae.</p