In this paper, we present some fixed point results for generalized θ‐ϕ‐contraction in the framework of α, η−compete rectangular b‐metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example.
The aim of this paper is to introduce a notion of
ϕ
,
F
-contraction defined on a metric space with
w
-distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.
In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of
θ
-contraction and
θ
−
ϕ
-contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.
The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of
θ
‐
ϕ
-contraction in metric spaces, introduced by Zheng et al., we present the notion of
θ
‐
ϕ
-contraction in
b
-rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.
In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced.In this paper, we present the notion of (phi,F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.
In the present work, for a unital C * -algebra A, we introduce the notion of (α A , η A )-C * -algebra valued b-quasi-metric spaces. Also, we discuss the existence and uniqueness of fixed points for a self-mapping defined on a such space. Our results extend and supplement several recent results in the literature. Some non-trivial examples are given to illustrate our results.
This paper is aimed to the notion of $\theta-\phi-$contraction defined on a metric space with $w-$distance. Moreover, fixed point theorems are given in this framework. Some illustrative examples are provided to advocate the usability of our results.As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations.
In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality as follows:for all distinct x, y, u, v ∈ X with the function α : X × X → [1, ∞[. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.