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On the uniqueness of continuous solutions of functional equations

100%

Gaweł B.

Annales Polonici Mathematici

1994-1995

tom 60

nr 3

231-239

We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities (1) ψ(f(x)) ≤ β(x,ψ(x)) and (2) α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)), where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation (3) φ(f(x)) = g(x,φ(x)), where Y denotes an arbitrary metric space.

A Generalization of m-Convexity and a Sandwich Theorem

75%

Lara T., Matkowski J., Merentes N., Quintero R., Wróbel M.

Annales Mathematicae Silesianae

2017

tom 31

nr 1

107-126

Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.

Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^p$-norm

51%

Matkowski J., Pycia M.

Annales Polonici Mathematici

1994-1995

tom 60

nr 3

221-230

Let a and b be fixed real numbers such that 0 < min{a,b} < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that $limsup_{t → 0+} f(t) ≤ 0$ must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the $L^p$-norm.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Annales Mathematicae Silesianae

2 Matkowski J.

1 Gaweł B.

1 Lara T.

1 Merentes N.

1 Pycia M.

1 Quintero R.

1 Wróbel M.

1 2017

2 1995

Wyniki wyszukiwania

On the uniqueness of continuous solutions of functional equations

A Generalization of m-Convexity and a Sandwich Theorem

Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^p$-norm