Application to Lipschitzian and Integral Systems via a Quadruple Coincidence Point in Fuzzy Metric Spaces

In this paper, the results of a quadruple coincidence point (QCP) are established for commuting mapping in the setting of fuzzy metric spaces (FMSs) without using a partially ordered set. In addition, several related results are presented in order to generalize some of the prior findings in this area. Finally, to support and enhance our theoretical ideas, non-trivial examples and applications for finding a unique solution for Lipschitzian and integral quadruple systems are discussed.This work was supported in part by the Basque Government under Grant IT1207-19

Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.This work was supported in part by the Basque Government under Grant IT1207-19

PPF-Dependent Fixed Point Results for New Multi-Valued Generalized F-Contraction in the Razumikhin Class with an Application

In this paper, a new multi-valued generalized F-contraction mapping is given. Using it, the existence of PPF-dependent fixed point for such mappings in the Razumikhin class is obtained. Moreover, an application for nonlinear integral equations with delay is presented here to illustrate the usability of the obtained results

A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ —norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.This work was supported in part by the Basque Government under Grant IT1207-19

Advanced Algorithms and Common Solutions to Variational Inequalities

The paper aims to present advanced algorithms arising out of adding the inertial technical and shrinking projection terms to ordinary parallel and cyclic hybrid inertial sub-gradient extra-gradient algorithms (for short, PCHISE). Via these algorithms, common solutions of variational inequality problems (CSVIP) and strong convergence results are obtained in Hilbert spaces. The structure of this problem is to find a solution to a system of unrelated VI fronting for set-valued mappings. To clarify the acceleration, effectiveness, and performance of our parallel and cyclic algorithms, numerical contributions have been incorporated. In this direction, our results unify and generalize some related papers in the literature.This work was supported in part by the Basque Government under Grant IT1207-19

A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations

This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive mappings (RSTN mappings, for short). Additionally, we demonstrate that for almost contraction mappings, the proposed algorithm converges faster than a variety of other current iterative schemes. Furthermore, the new iterative scheme’s ω2—stability result is established and a corroborating example is given to clarify the concept of ω2—stability. Moreover, weak as well as a number of strong convergence results are demonstrated for our new iterative approach for fixed points of RSTN mappings. Further, to demonstrate the effectiveness of our new iterative strategy, we also conduct a numerical experiment. Our major finding is applied to demonstrate that the two-dimensional (2D) Volterra integral equation has a solution. Additionally, a comprehensive example for validating the outcome of our application is provided. Our results expand and generalize a number of relevant results in the literature.This work was supported in part by the Basque Government under Grant IT1555-22

Differences in oral health status in elite athletes according to sport modalities

Oral health status may affect physical and sports performance. The purpose of this study was to assess the oral health status and oral health habits of elite athletes according to the performed sports type. A sample of 186 elite athletes divided into individual sports (n = 74; 53 men and 21 women; 24.9 ± 9.3 years) and team sports (n = 112; 97 men and 15 women; 24.5 ± 4.8 years) participated in the study. The decayed, missing, and filled teeth index (DMFT), the oral health impact profile (OHIP), and the diet assessment of caries risk (DACR) were evaluated to assess their oral health status. Athletes in individual modalities had a lower number in total teeth, healthy teeth, and restoration index (p < 0.05). Furthermore, this group showed a greater number of missing (p < 0.001) and decayed teeth (p < 0.05) and a greater DMFT index (p < 0.001). A relationship between sports modality and prevalence of malocclusions (p < 0.01), periodontal plaque (p < 0.05), and the habit of consuming energy drinks (p < 0.05) was also highlighted. Elite athletes who compete in individual sports presented a worse oral situation

Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives

The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness findings are obtained using a fixed point theorem of the type of Kransnoselskii. In keeping with this, many forms of Hyers-Ulam stability are examined. Ultimately, to support main results, an example is provided.This work was supported in part by the Basque Government under Grant IT1555-22

Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

The goal of this paper is to present a new class of contraction mappings, so-called -contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for -contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.This work was supported in part by the Basque Government under Grant IT1555-22

Fixed Point Approaches for Multi-Valued Prešić Multi-Step Iterative Mappings with Applications

The purpose of this paper is to present some fixed point approaches for multi-valued Prešić k-step iterative-type mappings on a metric space. Furthermore, some corollaries are obtained to unify and extend many symmetrical results in the literature. Moreover, two examples are provided to support the main result. Ultimately, as potential applications, some contributions of integral type are investigated and the existence of a solution to the second-order boundary value problem (BVP) is presented.This work was supported in part by the Basque Government under grant IT1555-22