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Mathematics, Vol. 7, Pages 1125: Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces (2019)

Sang Og Kim, John Michael Rassias

MDPI

In: Mathematics

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Publikationsdatum: 2019

Beschreibung: In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without Δ 2 -conditions. We study the same problem in fuzzy Banach spaces and β -homogeneous Banach spaces. We show the hyperstability of the functional equation associated with the Jordan triple product in fuzzy Banach algebras. The obtained results can be applied to differential and integral equations with kernels of non-power types.

Digitale ISSN: 2227-7390

Thema: Mathematik

Publiziert von MDPI

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Stability of the Fréchet Equation in Quasi-Banach Spaces (2020)

Kim, Sang Og

Molecular Diversity Preservation International

In: Mathematics. 2020; 8(4): 490. Published 2020 Apr 01. doi: 10.3390/math8040490.

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Publikationsdatum: 2020-04-01

Beschreibung: We investigate the Hyers–Ulam stability of the well-known Fréchet functional equation that comes from a characterization of inner product spaces. We also show its hyperstability on a restricted domain. We work in the framework of quasi-Banach spaces. In the proof, a fixed point theorem due to Dung and Hang, which is an extension of a fixed point theorem in Banach spaces, plays a main role.

Digitale ISSN: 2227-7390

Thema: Mathematik

Publiziert von Molecular Diversity Preservation International

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F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications (2019)

Asif, Awais ; Nazam, Muhammad ; Arshad, Muhammad ; [weitere]

Molecular Diversity Preservation International

In: Mathematics. 2019; 7(7): 586. Published 2019 Jun 30. doi: 10.3390/math7070586.

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Publikationsdatum: 2019-06-30

Beschreibung: In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

Digitale ISSN: 2227-7390

Thema: Mathematik