Refined stability of additive and quadratic functional equations in modular spaces

DOI10.1186/s13660-017-1422-zzbMath1365.39012OpenAlexW2698184044WikidataQ33844748 ScholiaQ33844748MaRDI QIDQ2360401

Hark-Mahn Kim, Hwan-Yong Shin

Publication date: 3 July 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-017-1422-z

zbMATH Keywords

Hyers-Ulam stabilityFatou propertyconvex modular\(\Delta_{2}\)-conditionmodular functional

Mathematics Subject Classification ID

Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functional equations for functions with more general domains and/or ranges (39B52) Systems of functional equations and inequalities (39B72)

Related Items (8)

Approximate cubic Lie derivations on \(\rho\)-complete convex modular algebras ⋮ Approximate Generalized Additive-Quadratic Functional Equations on Ternary Banach Algebras ⋮ Unnamed Item ⋮ Two multi-cubic functional equations and some results on the stability in modular spaces ⋮ Approximate homomorphisms from ternary semigroups to modular spaces ⋮ Stability of various functional equations in non-Archimedean \((n,\beta)\)-normed spaces ⋮ Functional equation and its modular stability with and without Δp-condition ⋮ Stability of additive-quadratic 3D functional equation in modular spaces by direct method

Cites Work

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• Optimal Hyers-Ulam's constant for the linear differential equations
• Applications of fixed point theorems to the Hyers-Ulam stability of functional equations -- a survey
• On the generalized Ulam-Hyers-Rassias stability of quadratic mappings in modular spaces without \(\Delta_2\)-conditions
• Asymptotic aspect of derivations in Banach algebras
• Orlicz spaces and modular spaces
• On the representation of complemented modular lattices
• General stability of functional equations of linear type
• Quasicontraction mappings in modular spaces without \(\Delta_2\)-condition
• Modular interpolation spaces. I
• Modular curves and the Eisenstein ideal
• Generalized stability of the Cauchy functional equation
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• A fixed point approach to stability of functional equations in modular spaces
• On Conjugate Spaces of Nakano Spaces
• The Stability of Certain Functional Equations
• On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces
• Note on a Stability Theorem
• On the Stability of the Linear Functional Equation

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