Coincidence Point 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.

A Fixed Point Theorem for Non-Self Mappings of Rational Type in 𝔟−Multiplicative Metric Spaces with Application to Integral Equations

Objectives: To prove fixed point theorem for non-self mappings of rational type in -multiplicative metric spaces and apply the theorem to solve integral equations. Method: Multiplicative metrically convex is defined in the context of - multiplicative metric spaces to prove fixed point theorems for pairs of non-self mappings using rational type contraction. Findings: The theorem demonstrates that under certain rational type contraction, a unique fixed point exists for non-self mappings in -multiplicative metric spaces. Applications of integral equations shown improved convergence and solution accuracy. Novelty: First fixed point theorem for non-self mappings in -multiplicative metric spaces, introducing a new approach to solving Volterra-Hammerstein integral equations. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: Coincidence Point, Nonself Mappings, Rational Type contraction, b-Multiplicative Metric Spaces (b-m ́ms), Volterra-Hammerstein integral equations

Exploring Profit Opportunities in Intuitionistic Fuzzy Metric Spaces via Edelstein Type Mappings

This paper establishes a break-even point theorem concerning a set of mappings adhering to an Edelstein-type contractive criterian within intuitionistic fuzzy metric domains. It explores the break-even analysis within a straightforward total cost-revenue model applicable to dynamic businesses. Utilizing the coincident point theorem within intuitionistic fuzzy metric space, the study demonstrates the inclination of profit-sensitive (or loss-sensitive) dynamic businesses towards their respective break-even points.

The Difference Between the Theory of Conformity and Neo-Confucianism in the View of Truth

In philosophical theory, the understanding of "truth" can be divided into axiological truth and epistemological truth. The truth in the axiological sense mainly involves the problem of meaning and value, while the truth in the epistemological sense involves the problem of the conformity between the subject of knowledge and the object of knowledge or the objective reality. From the epistemological point of view, we can clarify the difference between the coincidence theory and the Chinese Neo-Confucianism in the view of truth so that we can not only explain the truth of each theory but also understand the harmonious relationship between the two views of truth.

Method of Search Functionals and Its Applications in Fixed Point and Coincidence Theory

Method of Search Functionals and Its Applications in Fixed Point and Coincidence Theory

High-Accuracy Phase Frequency Detection Technology Based on BDS Time and Frequency Signals.

For the time and frequency signals of Beidou satellites, a high-accuracy phase frequency detection technology based on phase group synchronization is proposed. Using the Beidou receiver and satellite signals as the frequency standard and the measured signals, respectively. The Beidou receiver and the satellite signals are sent to the phase coincidence detector of the different frequencies to generate a phase coincidence point pulse, which is sent to the different frequency phase detector as a control signal to generate the phase differences between the Beidou receiver and satellite signals, and then complete the high-accuracy phase synchronization between the Beidou receiver and satellite signals. Experimental results show that when the delay resolution reaches ps level, the phase synchronization accuracy of the system can reach 10 ps, which has the characteristics of small phase noise, low development cost, simple circuit structure, and high synchronization accuracy compared with the traditional phase synchronization technologies. Therefore, it would be widely used in satellite positioning, astrometry, precision navigation, aerospace, satellite launch, power transmission, communications, radar, and other high-tech fields.

Optimal design of an inclined barrier for performance improvement of an oscillating water column device with an artificial neural network model

An oscillating water column (OWC) device with a surface-piercing inclined barrier has been studied in irregular waves. This study is to determine the optimal shape of an inclined barrier utilizing an Artificial Neural Network (ANN) model for the performance enhancement of the conventional OWC system. We employed the dual boundary element method (DBEM) as our numerical approach, which resolves two separate boundary integral equations (singular and hyper-singular) formulated at the coincident source points situated on either side of the degenerate barrier boundary. The design parameters affecting the performance of the OWC system have been optimized to maximize the power extraction using the trained ANN model. The training dataset was prepared using the DBEM, which is then used to train and validate the ANN model. Subsequently, the trained model was employed to make predictions using a broader dataset to identify the optimal combination of design parameters that maximize the conversion efficiency. The findings reveal that the well-trained ANN model can learn complex nonlinear relationships, make good predictions with high accuracy using a larger dataset of input conditions, and offer the optimal values of an inclined barrier appropriate for the wave conditions at the sea installation site.

The stationary Klein-Gordon equation with a delta-like source: A generalized function approach

This work aims to initiate a discussion on finding solutions to non-homogeneous differential equations in terms of generalized functions. For simplicity, we conduct the analysis within the specific context of the stationary Klein-Gordon equation with a point-like source, identifying a generalized function that solves such an equation and aligns with the solution obtained through the Fourier approach with dimensional regularization. In addition to being regular at the source singularity, a notable advantage of our solution is its presentation as a single expression, eliminating the need for piecewise definitions. The arguments presented here are applicable to a broader range of situations, offering a novel approach to addressing divergences in field theories using generalized functions. Moreover, we anticipate that the approach introduced in this work could provide a new method for handling Green functions regularized at coincident points, thereby simplifying the renormalization process in a wide range of theories.

Coincidence Point and Fixed Point Theorems in Dualistic Partial Metric Space

Coincidence Point and Fixed Point Theorems in Dualistic Partial Metric Space

Fixed-Point Results of Generalized (ϕ,Ψ)-Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations

In this manuscript, we prove numerous results concerning fixed points, common fixed points, coincidence points, coupled coincidence points, and coupled common fixed points for (ϕ,Ψ)-contractive mappings in the framework of partially ordered controlled metric spaces. Our findings introduce a novel perspective on this mathematical context, and we illustrate the uniqueness of our findings through various explanatory examples. Also, we apply the main result to find the existence and uniqueness of the solution of the system of integral equations as an application.

Coincidence Point Results for a New Class of Fuzzy Contractive Mappings

This work is mainly aimed to enhance the concept of fuzzy Z-contractive mapping [11] by establish a different contraction called fuzzy (Z,g)- contraction. we obtain some sufficient conditions for the existence and uniqueness of point of coincidence of fuzzy (Z,g)- contraction mappings in the context of fuzzy metric spaces and prove some intriguing results.

PARADIGMS OF RESEARCH IN HYBRID ARTISTIC PRACTICES

The context in which artistic practices are developed today requires a constant preoccupation with the challenges and commitments of artistic research, an intrinsic condition of these endeavors. Artistic research supports many points of coincidence, interaction, or overlap with the principles of scientific research, although they are characterized by a series of specific parameters. Due to the particularities of artistic research, art that questions topics of global interest (as happens in the case of sustainability, ecology or technology) is the art of our time, and the communication of these positions presupposes the development of ideas through research. The present text establishes a series of parameters related to engagement in artistic research, approached through the prism of representative contemporary artistic practices.

Fixed Point and Coincidence Point Theorems in Dualistic Partial Metric Spaces

In this paper, motivated by Fulga and Proca [1], we define the notion of dualistic E-contraction, generalized dualistic E-contraction, and Dass-Gupta dualistic rational E-contraction. We establish some new fixed-point theorems for E-contraction, generalized dualistic E-contraction, and Dass-Gupta dualistic rational E-contraction in a DPM space. Also, we define dualistic E\(\Delta\) -contraction, generalized dualistic E\(\Delta\)-contraction, and Dass-Gupta dualistic rational E\(\Delta\) -contraction. We establish some common fixed-point theorems for E\(\Delta\) -contraction, generalized dualistic E\(\Delta\)-contraction and Dass-Gupta dualistic rational E\(\Delta\)-contraction in the setting of DPM spaces. Our results extend and generalize some well-known results of [1] and [2]. We also provide an example that shows the usefulness of these contractions.

Fuzzy Metric Spaces: Optimizing Coincidence and Proximity Points

Our manuscript puts forward two novel fuzzy proximal contractive conditions. First, we present two variants of fuzzy α-proximal quasi-H-contractions and establish optimal coincidence point outcomes for these contractions in fuzzy metric space. This manuscript’s second part proposes the fuzzy ψ-contraction for a multivalued mapping equipped with fuzzy weak P-property and achieves the best proximity point outcome in strong fuzzy metric space. The findings of this study broaden and generalize some existing research results.

Stability and Data Dependence Results for Jungck-type Iteration Scheme

We propose and study a new Jungck-type iteration scheme to approximate coincidence points of contractive mappings. The strong convergence, stability, and data dependency results have been discussed. Numerical experiments demonstrate that the newly introduced Jungck-type iteration scheme yields a higher convergence rate in comparison with other Jungck-type iteration schemes available in the literature.

A new approach to coincidence points and common fixed points under a homotopy of families of mappings in b-metric spaces

In this paper, we derive coincidence point and common fixed point results under order homotopies of families of mappings in partially ordered [Formula: see text]-metric spaces.

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings.

Improving the Feedforward Component for Recent Variants of Predictive Functional Control

A recent study demonstrated that the use of feedforward information with conventional Predictive Functional Control (PFC) leads to unexpected inconsistencies, with subsequent negative impacts on tuning and behaviour. A proposal was made to define the coincident point differently and shown to reduce the lag in the closed-loop PFC responses and applied to some systems with benign dynamics. Other recent work has looked at parameterisations of the future input to deal with challenging open-loop dynamics and significantly extended the range of problems for which PFC can be effective. This paper combines the two concepts, and thus proposes an algorithm that has both more effective and simple tuning than original PFC as well as being applicable to a range of challenging dynamics.

3-Dimensional computational analysis of [formula omitted]-contraction in GV-fuzzy metric spaces with applications

It is a well known fact that contraction conditions play a major role in composing coincidence point results. In present work, a new ϕ-contraction is being corroborated to yield coupled coincidence points in partially ordered GV-fuzzy metric spaces. Due to the significant feature of H-type t-norm, in this communication, we endue GV-fuzzy metric spaces with this t-norm. We use the mixed monotone property of mappings with regard to partial ordering. Present work generalizes some already existing results. An applied example is also formulated to cast the 3-dimensional analysis of ϕ-contraction utilized in the main result. Computational analysis of the illustrative example has been done using the software MATLAB version R2022b which shows the experimental verification of our work. Furthermore, applications to the solution of the system of Fredholm type integral equations and solution of the system of equations in dynamic programming accords the validity of the present work. Endmost, the concluding remark projects the significance of current work.

Common fixed points for ($ \kappa _{G_{m}} $)-contractions with applications

<abstract><p>In this publication, our objective was to introduce and establish the concepts of $ \kappa _{G_{m}} $-contraction and generalized $ (\alpha, \kappa _{G_{m}}) $-contraction in complete $ G_{m} $-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis.</p></abstract>