In this paper, we introduce the concept of orthogonal contractive mappings and prove some fixed point theorems for such contractions. We establish our results in orthogonal bounded complete metric spaces via the notion of $tau-$distances. Moreover, an application to a differential equation is given.

https://ijnaa.semnan.ac.ir/article_5317_74c32927394128ad87f47458c067009d.pdf

Fixed point theorems on orthogonal complete metric spaces with an application

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

/pdf/banach-fixed-point-theorem-on-orthogonal-cone-metric-spaces-1gp5wrci7z.pdf

Banach fixed point theorem on orthogonal cone metric spaces

In this paper, a new class of nonexpansive mappings is defined and some fixed point theorems for such newly type are proved in the setting of bounded metric spaces without using neither the compactness nor the so-called uniform convexity. Our theorems generalize and improve many known results in the fixed point theory. Furthermore, we apply the main results to show the existence and uniqueness of a solution for a differential equation.

New contribution in fixed point theory via an auxiliary function with an application

\n We prove that the restriction of a given orthogonal-complete metric space to the closure of the orbit induced by the origin point with respect to an orthogonal-preserving and orthogonal-continuous map is a complete metric space. Then we show that many existence results on fixed points in orthogonal-complete metric spaces can be proved by using the corresponding existence results in complete metric spaces.

Notes on orthogonal-complete metric spaces

Fixed Point Results for Condensing Operators via Measure of Non-Compactness

In this paper, we prove some fixed point results for multivalued mappings in bounded metric spaces via symmetric spaces. Moreover an application to an integral inclusion is given.

Fixed point results for new type of multivalued mappings in bounded metric spaces with an application

The main purpose of this paper is to prove a new fixed theorem for selfmapping of a metric space . As applications, we get a new fixed point result for shrinking or contractive maps and a fixed point theorem for a new class of weakly contractive selfmappings of a bounded metric space , where the auxiliary function satisfies and .

/pdf/fixed-point-theorems-for-contractive-selfmappings-of-a-2eykmghwdp.pdf

Fixed Point Theorems for Contractive Selfmappings of a Bounded Metric Space

In this paper, we define the notion of generalized orthogonal sets by extending orthogonal sets. Also, we introduce the concept of 
$$\perp _{\psi F}$$

-contractions, which generalizes 
$$\perp _{F}$$

 contractions. For such contractions, some fixed point theorems are proved. Moreover, an application to a differential equation is given.

$$\perp _{\psi F}$$ ⊥ ψ F -contractions and some fixed point results on generalized orthogonal sets

In this paper, we first prove a new common fixed point in general topological spaces with a τ-distance. From this result, we establish two common fixed points for two new classes of contractive sel...

Youssef Touail

Papers

Fixed point results for new type of multivalued mappings in bounded metric spaces with an application

Fixed Point Theorems for Contractive Selfmappings of a Bounded Metric Space

$$\perp _{\psi F}$$ ⊥ ψ F -contractions and some fixed point results on generalized orthogonal sets

Some new common fixed point theorems for contractive selfmappings with applications

Fixed point theorems on orthogonal complete metric spaces with an application