Author:
Marraffa Valeria,Satco Bianca
Abstract
AbstractIn this paper, convergence theorems involving convex inequalities of Copson’s type (less restrictive than monotonicity assumptions) are given for varying measures, when imposing convexity conditions on the integrable functions or on the measures. Consequently, a continuous dependence result for a wide class of differential equations with many interesting applications, namely measure differential equations (including Stieltjes differential equations, generalized differential problems, impulsive differential equations with finitely or countably many impulses and also dynamic equations on time scales) is provided.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Area, I., Fernández, F.J., Nieto, J.J., Tojo, F.A.F.: Concept and solution of digital twin based on a Stieltjes differential equation, Math. Methods Appl. Sci., (2022)
2. Avendaño-Garrido, M.L., Gabriel-Argüelles, J.R., Torres Quintana, L., González-Hernández, J.: An approximation scheme for the Kantorovich-Rubinstein problem on compact spaces. J. Numer. Math. 26(2), 63–75 (2018)
3. Bruckner, A.M., Bruckner, J.B., Thomson, B.S.: Real Analysis. Prentice-Hall, Upper Saddle River (1997)
4. Copson, E.T.: On a generalisation of monotonic sequences. Proc. Edinb. Math. Soc. 17, 159–164 (1970)
5. Costarelli, D., Croitoru, A., Gavriluţ, A., Iosif, A., Sambucini, A.R.: The Riemann-Lebesgue integral of interval-valued multifunctions. Mathematics 8(12), 1–17 (2020)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献