General form of $$$(\lambda,\varphi)$$$-additive operators on spaces of $$$L$$$-space-valued functions

V.F. Babenko (Oles Honchar Dnipro National University),
V.V. Babenko (Drake University),
O.V. Kovalenko (Oles Honchar Dnipro National University),
N.V. Parfinovych (Oles Honchar Dnipro National University),


The goal of the article is to characterize continuous $$$(\lambda,\varphi)$$$-additive operators acting on measurable bounded functions with values in $$$L$$$-spaces. As an application, we prove a sharp Ostrowski type inequality for such operators.


$$$L$$$-space; $$$(\lambda,\varphi)$$$-additive operator

Full Text:



Anastassiou G.A. "Fuzzy Ostrowski type inequalities", Comput. Appl. Math., 2003; 22(2): рр. 279-292. doi:10.1590/S0101-82052003000200007

Aseev S.M. "Quasilinear operators and their application in the theory of multivalued mappings", Proc. Steklov Inst. Math., 1986; 167: pp. 23-52. (in Russian)

Babenko V. "Calculus and nonlinear integral equations for functions with values in L-spaces", Anal. Math., 2019; 45: pp. 727-755. doi:10.1007/s10476-019-0004-3

Babenko V., Babenko V., Kovalenko O. "Optimal recovery of monotone operators in partially ordered L-spaces", Numer. Func. Anal. Opt., 2020; 41(11): pp. 1373-1397. doi:10.1080/01630563.2020.1775251

Babenko V., Babenko V., Kovalenko O. "Korneichuk-Stechkin Lemma, Ostrowski and Landau inequalities, and optimal recovery problems for L-space-valued functions", arXiv, 2020. arXiv:2006.14581

Babenko V., Babenko V., Kovalenko O., Polishchuk M. "Optimal recovery of operators in function L-spaces", Anal. Math., 2021; 47: pp. 13-32. doi:10.1007/s10476-021-0065-y

Chalco-Cano Y., Flores-Franulic A., Román-Flores H. "Ostrowski type inequalities for interval-valued functions using generalized Hukuhara derivative", Comput. Appl. Math., 2012; 31(3): pp. 457-472. doi:10.1590/S1807-03022012000300002

Dunford N., Schwartz J.T. Linear Operators, Part I: General Theory, Interscience Publishers, 1958.

Kovalenko O. "On optimal recovery of integrals of random processes", J. Math. Anal. Appl., 2020; 487(1): 123949. doi:10.1016/j.jmaa.2020.123949

Ostrowski A. "Über die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert", Comment. Math. Hel., 1937; 10: pp. 226-227. (in German) doi:10.1007/BF01214290

Vahrameev S.A. Applied Mathematics and Mathematical Software of Computers, MSU Publisher, 1980.

Warga J. Optimal Control of Differential and Functional Equations, Acad. Press, 1972.




  • There are currently no refbacks.

Copyright (c) 2022 V.F. Babenko, V.V. Babenko, O.V. Kovalenko, N.V. Parfinovych

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Registered in


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991