scholarly journals Stability of Unbounded Differential Equations in Menger k-Normed Spaces: A Fixed Point Technique

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 400 ◽  
Author(s):  
Masoumeh Madadi ◽  
Reza Saadati ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Normed Spaces ◽  
Fixed Point Technique ◽  
Rassias Stability

We attempt to solve differential equations υ ′ ( ν ) = Γ ( ν , υ ( ν ) ) and use the fixed point technique to prove its Hyers–Ulam–Rassias stability in Menger k-normed spaces.

scholarly journals Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Shen ◽  
Yaoyao Lan ◽  
Wei Chen
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Functional Equations ◽  
Cauchy Type ◽  
Upper Semicontinuous ◽  
Real Separable Banach Space ◽  
Fixed Point Technique ◽  
Supremum Metric ◽  
Stability Results ◽  
Rassias Stability

LetYbe a real separable Banach space and let𝒦CY,d∞be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets ofYequipped with the supremum metricd∞. In this paper, we introduce several types of additive fuzzy set-valued functional equations in𝒦CY,d∞. Using the fixed point technique, we discuss the Hyers-Ulam-Rassias stability of three types additive fuzzy set-valued functional equations, that is, the generalized Cauchy type, the Jensen type, and the Cauchy-Jensen type additive fuzzy set-valued functional equations. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.

scholarly journals A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1117
Author(s):  
Maryam Ramezani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results.

scholarly journals A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 647 ◽  
Author(s):  
Kui Liu ◽  
Michal Fečkan ◽  
JinRong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Compact Interval ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Stability Results ◽  
Rassias Stability

In this paper, we study Hyers–Ulam and Hyers–Ulam–Rassias stability of nonlinear Caputo–Fabrizio fractional differential equations on a noncompact interval. We extend the corresponding uniqueness and stability results on a compact interval. Two examples are given to illustrate our main results.

Ulam–Hyers stabilities of a generalized composite functional equation in non-Archimedean spaces

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Pasupathi Narasimman ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Normed Spaces ◽  
Composite Functional Equation ◽  
Rassias Stability

AbstractIn this paper, we introduce a new generalized composite functional equation and prove its Hyers–Ulam–Rassias stability, Ulam–Găvruta–Rassias stability and Ulam–J. Rassias stability in non-Archimedean normed spaces using a fixed point method.

scholarly journals Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

2021 ◽  
Vol 5 (1) ◽  
pp. 22
Author(s):  
Kulandhaivel Karthikeyan ◽  
Amar Debbouche ◽  
Delfim F. M. Torres
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sectorial Operators ◽  
Fundamental Properties ◽  
Almost Sectorial Operators ◽  
Fixed Point Technique

In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.

scholarly journals Stability analysis for discrete time abstract fractional differential equations

2021 ◽  
Vol 24 (1) ◽  
pp. 307-323
Author(s):  
Jia Wei He ◽  
Yong Zhou
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Discrete Time ◽  
Difference Operator ◽  
Closed Linear Operator ◽  
Abstract Form ◽  
Fractional Differential ◽  
Stable Solutions ◽  
Fixed Point Technique ◽  
Rassias Stability

Abstract In this paper, we consider a discrete-time fractional model of abstract form involving the Riemann-Liouville-like difference operator. On account of the C 0-semigroups generated by a closed linear operator A and based on a distinguished class of sequences of operators, we show the existence of stable solutions for the nonlinear Cauchy problem by means of fixed point technique and the compact method. Moreover, we also establish the Ulam-Hyers-Rassias stability of the proposed problem. Two examples are presented to explain the main results.

scholarly journals On the new Hyers–Ulam–Rassias stability of the generalized cubic set-valued mapping in the incomplete normed spaces

2021 ◽  
Vol 26 (5) ◽  
pp. 821-841
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Normed Spaces ◽  
Set Valued Mapping ◽  
The Stability ◽  
Stability Definition ◽  
Rassias Stability

We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study a generalized cubic set-valued mapping in normed spaces. In order to achieve our goals, we have applied a brand new fixed point alternative. Meanwhile, we have obtained a practicable example demonstrating the stability of a cubic mapping that is not defined as stable according to the previously applied methods and procedures.

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