This paper presents a novel approach to Caristi's fixed point (FP) theorem (CFT) within the context of symmetric (SM) spaces. The study establishes the conditions under which CFT extends on-complete regular symmetric spaces, particularly focusing on the notion of-completeness and the extending CFT inequality. The-completeness concept is examined, revealing its significance in the analysis of FPs. Some previous finding, including Ekeland's variational principle (EVP), Takahashi's minimization theorem and CFT in b-metric spaces, are developed. Moreover, many concrete examples are given to illustrate the results.

A document by Hamid Mottaghi Golshan. Click on the document to view its contents.

A document by Hamid Mottaghi Golshan. Click on the document to view its contents.

A document by Hamid Mottaghi Golshan. Click on the document to view its contents.

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.

A document by Hamid Mottaghi Golshan. Click on the document to view its contents.

A document by Hamid Mottaghi Golshan. Click on the document to view its contents.