Point Theorems In B-metric Spaces Research Articles

On Pair of Compatible Mappings and Coincidence Point Theorems in b-Metric Spaces

The main goal of this study is to give two different results for a couple of compatible self-mappings. The first result provides the necessary condition for the existence of a coincidence point for a pair of mappings that are partially weakly increasing in partially ordered b-metric spaces. Additionally, we establish a fixed point result in order to guarantee the uniqueness of common fixed points for pair of maps satisfying the b-(E.A.) Property. Our findings extends and improve well established results of existing literature. In order highlight the distinctiveness of our main theorems, two discrete examples with Tabular and Graphical representations are also presented.

Some common fixed point theorems in b-metric spaces via F-class function with applications

Some common fixed point theorems in b-metric spaces via F-class function with applications

Some common fixed point theorems in b-metric spaces under Geraghty-Berinde-Suzuki type contraction

Some common fixed point theorems in b-metric spaces under Geraghty-Berinde-Suzuki type contraction

Some New Fixed Point Theorems in b-Metric Spaces with Application

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results.

Some fixed point theorems for generalized Kannan type mappings in b-metric spaces

In this paper, we prove some fixed point theorems in b-metric spaces using subadditive altering distance function. Some of these results generalize many existing fixed point theorems for Kannan type mappings. The results are justified with suitable examples.

Best proximity point theorems in b-metric spaces

In this paper, we prove best proximity point theorems for types of cyclic b-contraction mappings in the setting of complete b-metric spaces which generalize some results in the current literature.

Fixed point theorems in b-metric spaces with applications to differential equations

In this paper, we present some fixed point theorems for a class of contractive mappings in b-metric spaces. We verify the T-stability of Picard’s iteration and the P property for such mappings. We also give an example to support our assertions. In addition, by using our results, we obtain the existence and uniqueness of solution to some ordinary differential equations with initial value conditions. Further, we provide the precise mathematical expressions of solutions to such equations.

Fixed point theorems in b-metric spaces and their applications to non-linear fractional differential and integral equations

In this paper, we modify L-cyclic $$(\alpha ,\beta )_s$$ -contractions and using this contraction, we prove fixed point theorems in the setting of b-metric spaces. As an application, we discuss the existence of a unique solution to non-linear fractional differential equation, 1 $$\begin{aligned} ^{c}D^{\sigma }(x(t))=f(t,x(t)),\ \ \text {for all}\ \ t\in (0,1), \end{aligned}$$ with the integral boundary conditions, $$\begin{aligned} x(0)=0,\ \ x(1)=\int _{0}^{\rho }x(r)\mathrm{d}r,\ \ \text {for all}\ \rho \in (0,1), \end{aligned}$$ where $$x\in C(\left[ 0,1\right] ,\mathbb {R})$$ , $$^{c}D^{\alpha }$$ denotes the Caputo fractional derivative of order $$\sigma \in (1,2]$$ , $$f : [0,1] \times \mathbb {R}\rightarrow \mathbb {R}$$ is a continuous function. Furthermore, we established existence result of a unique common solution to the system of non-linear quadratic integral equations, $$\begin{aligned}{\left\{ \begin{array}{ll} x(t)&{}= \int _{0}^{1}H(t,\tau )f_{1}(\tau ,x(\tau )) \mathrm{d}\tau ,\ \text {for all}~ t\in [0,1]; \\ x(t)&{}= \int _{0}^{1}H(t,\tau )f_{2}(\tau ,x(\tau )) \mathrm{d}\tau ,\ \text {for all}~ t\in [0,1], \end{array}\right. } \end{aligned}$$ where $$H : \left[ 0,1\right] \times \left[ 0,1\right] \rightarrow [0,\infty )$$ is continuous at $$t\in \left[ 0,1\right] $$ for every $$\tau \in \left[ 0,1\right] $$ and measurable at $$\tau \in \left[ 0,1\right] $$ for every $$t\in \left[ 0,1\right] $$ and $$f_{1}, f_{2}: \left[ 0,1\right] \times \mathbb {R}\rightarrow [0,\infty )$$ are continuous functions.

A common fixed point theorem of Jungck in rectangular b-metric spaces

We give a proof for the common fixed point theorem of Jungck in rectangular b-metric spaces. As a corollary, we obtain well known common fixed point theorems in b-metric spaces.

Fixed point and coincidence point theorems in b-metric spaces with applications

In this paper, we will consider the coincidence point problem for a pair of single-valued operators satisfying to some contraction and expansion type conditions. Existence, uniqueness and qualitative properties of the solution will be presented. The results are based on some fixed point theorems for nonlinear contractions in complete b-metric spaces. An application illustrates the theoretical results.

Geraghty and Ćirić type fixed point theorems in b-metric spaces

Geraghty and Ćirić type fixed point theorems in b-metric spaces

On relaxations of contraction constants and Caristi’s theorem in b-metric spaces

In this paper, the following facts are stated in the setting of b-metric spaces. (1) The contraction constant in the Banach contraction principle fully extends to [0, 1), but the contraction constants in Reich’s fixed point theorem and many other fixed point theorems do not fully extend to [0, 1), which answers the early stated question on transforming fixed point theorems in metric spaces to fixed point theorems in b-metric spaces. (2) Caristi’s theorem does not fully extend to b-metric spaces, which is a negative answer to a recent Kirk–Shahzad’s question (Remark 12.6) [Fixed Point Theory in Distance Spaces. Springer, 2014].