Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations

Amara, Khaled Ben; Berenguer, M.; Jeribi, Aref

doi:10.3390/math10224179

Cited by 2 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, for all bounded sets A ⊂ E, and then it is concluded that T is a densifying map, which is not correct (see [7, Sec 2.5.7], [11, Theorem 2.2] and [4,5,8] and previous example). If one adds assumption "there exist r 0 > 0 such that…”

mentioning

confidence: 99%

An existence result for implicit functional equations

Golshan

2023

Preprint

View full text Add to dashboard Cite

In this article, we attempt to provide a more general method based on Petryshyn’s fixed-point theorem to ensure the existence of solutions to implicit functional equations. These implicit functional equations include fractional, non-fractional, (fractional) stochastic integral equations, etc., and any combination of them in C( I). Some results regarding the existence of fixed points in implicit functional integral equations will be reviewed in the literature. We show that this general result unifies and improves many of the main results in the literature. To illustrate that our approach is more general than other methods, we present some concrete examples. Also, we apply our method to create new functional equations in practice and check the existence of solutions.

show abstract

mentioning

confidence: 99%

An existence result for implicit functional equations

Golshan

2023

Preprint

View full text Add to dashboard Cite

show abstract

On theoretical and numerical analysis of fractal--fractional non-linear hybrid differential equations

Shafiullah,

Shah,

Sarwar

et al. 2024

Nonlinear Engineering

View full text Add to dashboard Cite

Recently, fractals and fractional calculus have received much attention from researchers of various fields of science and engineering. Because the said area has been found applicable in modeling various real-world processes and phenomena. Hybrid differential equations (HDEs) play significant roles in mathematical modeling of various processes because the aforesaid equations incorporate different dynamical systems as specific cases. For instance, it is possible to model and describe non-homogeneous physical phenomena on using the said equations. Therefore, this research work is concerned with studying a class of nonlinear hybrid fractal–fractional differential equations. We develop the existence result for the qualitative study using a hybrid fixed point theorem. For the mentioned goal, a fixed point theory for the product of two operators is applied to deduce appropriate conditions for the existence of exactly one solution. Additionally, the stability result based on Ulam–Hyers is also deduced. The said stability results play an important role in numerical investigations. In addition, a numerical method based on Euler procedure is utilized to approximate the solution of the proposed problems. Various computational test problems are given to demonstrate the results. Also, using various fractal–fractional order values, several graphical presentations are given for the examples. The concerned analysis will help in investigating many real-world problems modeled using HDEs with fractal–fractional orders in the near future.

show abstract

Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations

Cited by 2 publications

References 27 publications

An existence result for implicit functional equations

An existence result for implicit functional equations

On theoretical and numerical analysis of fractal--fractional non-linear hybrid differential equations

Contact Info

Product

Resources

About