Using the fixed point method, we prove the Hyers–Ulam stability of a cubic and quartic functional equation and of an additive and quartic functional equation in matrix Banach algebras.

The genetic level differences between Brassica species can have potential impact on their performance under salt stress conditions together with Phosphorus and Potassium applications. In this study we hypothesized that certain level of salt stress mitigation can be done with applications of Phosphorus and Potassium solutions. Germinated seeds of Brassica juncea (var. Khanpur raya) and B. napus (Faisal canola), raised to 10 days seedlings stage and transferred to continuously aerated nutrient solution  For salt stress, applied NaCl @60 mM in the nutrient solution’ also applied phosphorus as potassium di hydrogen phosphate (PDP) @ 0 and 10 mM in triplicates. Khanpur raya and Faisal canola responded significantly (p< 0.01) to the application of PDP for growth and ions relations under salt stress and non-stress. Under stress conditions, shoot fresh mass (SFM) of Khanpur raya increased 10 percent with 10 mM of applied PDP than its control whereas SFM of Faisal canola increased 8 percent than its control. Root fresh mass (RFM) of Khanpur raya increased 8 percent with 10 mM of applied PDP than its control whereas RFM of Faisal canola increase 10 percent than its control. Dry mass of Khanpur raya increased 11 percent with 10 mM of applied PDP than its control whereas SDM of Faisal canola increased 6 percent than its control. Root dry mass (RDM) of Khanpur raya increased 18 percent with 10 Mm of applied PDP than its control whereas RDM of Faisal canola increased 19 percent than its control. In Khanpur raya Na+ /K+ ratio decreased 21 percent than the control, whereas this ratio decreased 24 percent in Faisal canola than its control. Under salt stress, physiological P-use in shoot and root of Khanpur raya increased 11 and 8 percent respectively than that of Faisal canola.

No abstract

No abstract