On superstability of exponential functional equations

Noori, Batool; Moghimi, M. B.; Najati, Abbas; Park, Choonkil; Lee, Jung Rye

doi:10.1186/s13660-021-02615-w

Cited by 4 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From that point forward, numerous stability problems for different functional equations have been explored in [6][7][8][9][10][11][12][13][14][15]. Later, the stability issues for different types of functional equations were investigated in [16,17].…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

Tamilvanan¹,

Alkhaldi

Agarwal

et al. 2023

Mathematics

View full text Add to dashboard Cite

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ-2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

show abstract

Section: Introductionmentioning

confidence: 99%

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

Tamilvanan¹,

Alkhaldi

Agarwal

et al. 2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Davydovych (Davydovych, 2018). Мany scientific researches today are devoted to the stability of functional equations (Rassias et al, 2012;Moslehian et al, 2007;Moszner, 2009;Saadati et al, 2011;Brzdek et al, 2011;Noori et al, 2021) and their applications (Russias, 2003;El-Hady,2019).…”

Section: Introductionmentioning

confidence: 99%

Inclusion of the Topic «the Simplest Functional Equations» in the Model Programs for Studying the Subject «algebra and the Beginnings of Analysis»

Бохонова¹,

Bokhonov²,

Matvieieva³

et al. 2023

FMO

View full text Add to dashboard Cite

Formulation of the problem. Analysis of the issue of including the topic "The simplest functional equations" in the model curricula for studying the subject "Algebra and the beginnings of analysis" for specialized classes with in-depth study of mathematics. A model curriculum studies the approximate sequence of achieving the expected learning outcomes, the content of the subject or integrated course, and the types of students’ educational activities. The inclusion of this topic aims to start a creative understanding of functional relationships existing in real systems and processes, in particular, ecological, economic, and social ones. Materials and methods. Theoretical method of analysis of methodical and educational literature on the researched issue; comparative analysis to understand different views on the problem; systematization and generalization to create recommendations for the content of the proposed topic, as well as formulating conclusions and integrating the pedagogical experience of authors who teach relevant disciplines in educational institutions of various levels. Results. The possible content of the topic "The simplest functional equations" in the model programs for studying the subject "Algebra and the beginnings of analysis", examples for an explanation by the teacher, and confirmation by students are proposed. For some examples, different approaches to their solution are proposed; convenient tables are provided for students to find partial solutions to some types of functional equations. Conclusions. The authors believe that the topic "The simplest functional equations" will be useful and acceptable for studying within the scope of the subject "Algebra and the beginnings of analysis" by students of specialized classes with an in-depth study of mathematics. Within the eleven-year school education, of course, it was impossible to find time to study this topic due to the saturation and density of the material necessary for study. But in the twelve-year New Ukrainian School, marked by a deeper differentiation of specialized education, the topic "The simplest functional equations" can strengthen the fundamentality of mathematical education in classes with in-depth study of mathematics, computer science, etc. Further research in this direction may concern the method of solving the simplest recurrent equations.

show abstract

“…In the past decades and recent years, various types of stability problems for different functional equations have been studied by many mathematicians (cf. e.g., [2,[8][9][10][11][12][13][14][15] and the bibliography quoted there).…”

Section: Introductionmentioning

confidence: 99%

Stability of a Bi-Jensen Functional Equation on Restricted Unbounded Domains and Some Asymptotic Behaviors

2022

Self Cite

View full text Add to dashboard Cite

In this paper, we give some properties of the bi-Jensen functional equation and investigate its Hyers–Ulam stability and hyperstability. We construct a function which is bi-Jensen and is not continuous. Additionally, we investigate the Hyers–Ulam stability of the bi-Jensen functional equation on some restricted unbounded domains. Finally, we apply the obtained results to study some interesting asymptotic behaviors of bi-Jensen functions.

show abstract

On superstability of exponential functional equations

Abstract: The aim of this paper is to prove the superstability of the following functional equations: $$\begin{aligned}& f \bigl(P(x,y) \bigr)= g(x)h(y), \\& f(x+y)=g(x)h(y). \end{aligned}$$ f ( P ( x , y ) … Show more

Cited by 4 publications

References 20 publications

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

Inclusion of the Topic «the Simplest Functional Equations» in the Model Programs for Studying the Subject «algebra and the Beginnings of Analysis»

Stability of a Bi-Jensen Functional Equation on Restricted Unbounded Domains and Some Asymptotic Behaviors

Contact Info

Product

Resources

About