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SGT derived from a marine actinomycete, S. tropica, was found to strictly function on β-sitosterol.
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Let δ be a strictly convex or strictly concave function on I. Suppose that g is a real-valued integrable function on Ω such that g ∈ I for almost all ω ∈ Ω and δ ∘ g ∈ L1.
Let be a real continuous strictly monotone function on and be a differentiable and strictly increasing function on.
then φ is called strictly concave function on D. We are now in the position to apply the topological degree and properties of strictly convex (concave) function to derive some new fixed point theorems for semi-closed 1-set-contractive operators and existence theorems of solutions for the equation Ax = μx which generalize a great deal of well-known results and relevant recent ones.
therefore is strictly increasing function on for each.
(ii)if is (strictly) concave function on, then (2.2).
then is strictly increasing function on for each.
(i if is (strictly) convex function on, then (2.1).
Let be a real continuous strictly monotone function on.
Note that (f(d)) is a strictly decreasing function on d.
Furthermore, Φ is a continuous convex and strictly increasing function on [ 0, ∞ ) (see [3]).
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