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In this paper, we introduce the concept of elliptic-valued b-metric spaces, extending the notions of elliptic-valued metric spaces and complex-valued metric spaces. We present several fixed-point results that involve rational and product terms within this novel space framework. To support our main findings, we offer numerical examples. Additionally, we demonstrate an application of Urysohn integral equations. [ABSTRACT FROM AUTHOR]

This article introduces the concept of generalized (ff F , b , ϕ ˘) contraction in the context of b -metric spaces by utilizing the idea of F contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existence of best proximity points for multi-valued (ff F , b , ϕ ˘) contractions in partially ordered b -metric spaces. The article provides examples to illustrate the main results and demonstrates the existence of solutions to a second-order differential equation and a fractional differential equation using the established theorems. Additionally, several corollaries are presented to show that the results generalize many existing fixed-point and best proximity point theorems. [ABSTRACT FROM AUTHOR]

In this publication, our objective was to introduce and establish the concepts of KGm-contraction and generalized (a, KGm)-contraction in complete Gm-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. [ABSTRACT FROM AUTHOR]

In this manuscript, utilizing interpolative contractions with fractional forms, some unique fixed-point results were studied in the context of extended b-metric spaces. For the validity of the presented results some examples are given. In the last section an existence theorem is provided to study the existence of a solution for the Fredholm integral equation. [ABSTRACT FROM AUTHOR]

Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation. [ABSTRACT FROM AUTHOR]

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β -neighborhoods (IHF β -neighborhoods) and intuitionistic hesitant fuzzy complementary β -neighborhoods (IHFC β -neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β -neighborhoods and IHFC β -neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. [ABSTRACT FROM AUTHOR]

This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of contraction to seek the existence of tripled best proximity point results. Here, using the new contraction and P-property, we generalize and extend results of W. Shatanawi and A. Pitea and prove the existence and uniqueness of some tripled best proximity point results. Examples are also given to support our results.