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In this paper, we introduced a new contraction principle via altering distance and $ C $-class functions with rational forms which extends and generalizes the existing version provided by Hasan Ranjbar et al. [H. Ranjbar, A. Niknam, A fixed point theorem in Hilbert $ C^\ast $-modules, Korean J. Math., 30 (2022), 297–304]. Specifically, the rational forms involved in the contraction condition we presented involve the $ p $-th power of the displacements which can exceed the second power mentioned in Hasan Ranjbar et al.'s paper. Moreover, we also proved a fixed point theorem for this type of contraction in the Hilbert $ C^\ast $-module. Some adequate examples were provided to support our results. As an application, we applied our result to prove the existence of a unique solution to an integral equation and a second-order $ (p, q) $-difference equation with integral boundary value conditions.

Abstract In this paper, we introduce two types of weak enriched contractions, namely weak enriched F $\mathcal{F}$ -contraction, weak enriched F ′ $\mathcal{F^{\prime}}$ -contraction, and k-fold averaged mapping based on Kirk’s iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk’s iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature.

Abstract Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection model. Alternative contraction mappings introduced by Chen (Symmetry 11:750, 2019) built a new model containing several mirrors in which the light reflected from a mirror does not go to the next mirror sequentially, and its path may diverge to any other mirror. The aim of this paper is to present a new variant of alternative contraction called alternative p-contraction and study its properties. The best proximity point result for such contractions under the alternative UC property is proved. An example to support the result proved herein is provided.

In the process of promoting demand-side management, the core stakeholder groups are government departments, power grid companies, and electricity users. Due to the different positions and conflicting interests of the three parties in the game, intense and complex battles will occur. This paper investigates a tripartite evolutionary game involving government, power grid companies, and electricity users in the context of demand-side management (DSM) and analyzes the dynamic interactions between government departments, power grid companies, and electricity users within the framework of DSM using evolutionary game theory. Using evolutionary game theory, we explore how incentives and strategic interactions among these three stakeholders evolve over time, affecting the stability of DSM policies. The model addresses the asymmetry in the decision-making process and examines the dynamic equilibrium outcomes under various scenarios. The results provide insights into the optimal design of incentive mechanisms to enhance DSM adoption. The findings offer practical recommendations to improve DSM policies, fostering balanced interests between government, grid companies, and users. This research contributes to a deeper understanding of strategic interactions in DSM, revealing how adaptive behaviors can enhance energy efficiency. It also underscores the importance of carefully designed incentive mechanisms in achieving long-term stability and cooperation among key stakeholders.

In this paper, we present new existence results for the quasi-variational inequality problem (QV I) in reflexive Banach spaces using the fixed point method with quasi-monotonicity and local upper sign-continuity assumptions. These results improve upon previous ones which only required a weaker monotonicity condition and did not impose compactness on the involved set.

Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions.

Abstract In this paper, we introduce two new concepts of F-contraction, called dual F ∗ $F^{*}$ -weak contraction and triple F ∗ $F^{*}$ -weak contraction, which generalize the existing contractions in the sense of Wardowski, Jleli and Samet as well as Skof. These new generalizations embed their roots in the aim devoted to extending the generalized Banach contraction conjuncture to the class of F-contraction type mappings with the use of multiple F-type functions. Furthermore, we establish the existence of a unique fixed point for such contractions under certain conditions. Fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates that can be expressed as functions of one independent variable. We apply our main result to weaken certain conditions on the fractional integral equations. Finally, we discuss the significance of our obtained results in comparison with certain renowned ones in the literature.

Abstract In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for ( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contractions, rational- ( γ , ψ , φ , ϕ ) $(\gamma , \psi ,\varphi ,\phi )$ contractions and almost- ( γ , ψ , φ , ϕ ) $(\gamma ,\psi , \varphi ,\phi )$ contractions and φ-fixed disc results for ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 1 contractions, ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 2 contractions, and ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 3 contractions in metric spaces. We generalize some existing φ-fixed point and φ-fixed circle results in the literature. Further, we give some examples to demonstrate the usefulness of our results and investigate the existence and uniqueness of solutions of nonlinear integral equations.

In this paper, our main aim is to present innovative fixed-point theorems that provide solutions to the fixed-circle problem with symmetric contractions. We accomplish this by employing operator enrichment techniques within the context of Banach spaces. Furthermore, we demonstrate the practical application of these theorems by showcasing their relevance to the rectified linear unit (ReLU) activation function. By exploring the connection between fixed points and activation functions, our work contributes to a deeper understanding of the behavior and properties of these fundamental mathematical concepts.

In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pairs of self-mappings within the framework of b-metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.

This paper deals with a well known open problem raised by Kannan (Bull. Calcutta Math. Soc., 60: 71–76, 1968) and B. E. Rhoades (Contemp. Math., 72: 233–245, 1988) on the existence of general contractions which have fixed points, but do not force the continuity at the fixed point. We propose some new affirmative solutions to this question using two new contractions called (ψ,φ)-A-contraction and (ψ,φ)-A′-contraction inspired by the results of H. Garai et al. (Applicable Analysis and Discrete Mathematics, 14(1): 33–54, 2020) and P. D. Proinov (J. Fixed Point Theory Appl. (2020) 22: 21). Some new fixed point and common fixed point results in compact metric spaces and also in complete metric spaces are proved in which the corresponding contractive mappings are not necessarily continuous at their fixed points. Moreover, we show that new solutions to characterize the completeness of metric spaces. Several examples are provided to verify the validity of our main results.

In this paper, we introduce α-admissible extended Z-contraction in the extended rectangular b-metric spaces, then we provide some other conditions in Theorem 3.1, which are different from that in Chifu et al. [1], and obtain the existence and uniqueness of fixed point in such spaces. Moreover, some examples are given to show the validity of our main theorems, and we give some corollaries related to our main results. As an application, we apply our main results to solve the existence of solutions for a class of boundary value problems of second order ordinary differential equations.

In this paper, firstly, we introduce some new generalizations of F−contraction, F−Suzuki contraction, and F−expanding mappings. Secondly, we prove the existence and uniqueness of the fixed points for these mappings. Finally, as an application of our main result, we investigate the existence of a unique solution of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order (1, 2).

In this paper, we prove some common fixed point theorems by exploring a new kind of generalized semi-compatibility and an implicit relation via inverse C−class functions. The results generalize, extend and improve the main results of [19, 21, 22, 23]. Moreover, some examples are given to illustrate the validity of our results.

The economic strength of a country is the external manifestation of its comprehensive national strength. In order to increase a country’s international influence, it must strengthen its own economic development. China’s economy is in a period of rapid development. At this stage, enterprise development is an important factor in promoting steady economic growth. However, economic management plays an important role in the development of an enterprise. Therefore, how to use effective economic management methods to promote the development of enterprises is very important. This method helps to enhance the competitiveness of enterprises and improve the economic efficiency of enterprises. This approach needs to get people’s attention. For productive enterprises, the biggest problem is that the economic benefits are not up to expectations. In addition, spending costs are always well over budget. In fact, this has a lot to do with business management. Before the market, economic system was reformed. The comprehensive management of productive enterprises is mostly extensive management. This makes the economic costs of certain links and details out of control. Therefore, effective management of the economy of a productive enterprise is critical. Although productive enterprises cannot be said to be highly profitable, their economic benefits are at least achievable. For productive enterprises, the most effective management method for the economy is refined management. This article starts from the perspective of improving the speed of enterprise development. Specifically, the starting point is to promote the improvement of the country’s comprehensive national strength. The article analyzes the inherent relationship between economic management and enterprise development, hoping it can provide positive help for China’s social and economic progress.

In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F−metric spaces. Further, we obtain the best proximity point result for generalized α−φ−proximal contractions in F−metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F−metric spaces via best proximity points.

This paper addresses a problem of global optimization in a non-Archimedean fuzzy metric space context without fuzzy P-property. Specifically, it concerns the determination of the fuzzy distance between two subsets of a non-Archimedean fuzzy metric space. Our approach to solving this problem is to find an optimal approximate solution to a fixed point equation. This approach has been well studied within a category of problems called proximity point problems. We explore some new types of (ψ−ϕ)-weak proximal contractions and investigate the existence of the unique best proximity point for such kinds of mappings. Subsequently, some fixed point results for corresponding contractions are proved, and some illustrative examples are presented to support the validity of the main results. Moreover, an interesting application in computer science, particularly in the domain of words has been provided. Our work is a fuzzy generalization of the proximity point problem by means of fuzzy fixed point method.

In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify F-contraction by developing F-rotative mapping and establish some fixed-point theorems. Finally, we apply our results to prove the existence of a solution of a non-linear fractional differential equation.

The purpose of this paper is to develop coupled fixed point theorems by C-class functions with mixed monotonicity, discuss the existence of the coupled fixed point of two mappings and obtain a coupled coincidence point theorem via inverse Ck-class functions in partially ordered H-metric spaces. This improves the existing results. In addition, some instances and an application are given to illustrate the usability and validity of the results.

In this paper, we firstly introduce a new notion of inverse Ck−class functions which extends the notion of inverse C−class functions introduced by Saleem et al., 2018. Secondly, some common fixed point theorems are stated under some compatible conditions such as weak semicompatible of type A, weak semicompatibility, and conditional semicompatibility in metric spaces. Moreover, we introduce a new kind of compatibility called Sτ−compatibility which is weaker than E.A. property and also present a common fixed point theorem in metric spaces via inverse Ck−class functions. Some examples are provided to support our results.

In this paper, we introduce some new types of extended Geraghty contractions, called (α,β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

In this paper, we present a new type of rational contraction in double controlled metric-like spaces and improve recent results of such spaces. Moreover, there is an example to verify the correctness of our results. Finally, we also obtain some new fixed point results, which can be derive directly from our main theorem.

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as a special submodel of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived, and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data, and the comparison is made with the Weibull and some of its well-known extensions such as Marshall–Olkin Weibull, alpha power-transformed Weibull, and Kumaraswamy Weibull distributions.

In this paper, we introduce two new concepts, generalized α-η-FZ-contraction and modified α-η-FZ-contraction, which unify several types of contractions in the context of fuzzy metric spaces. We discuss the existence and uniqueness results of such mappings in the setting of a complete fuzzy metric space in the sense of George and Veeramani and present several significant consequences of our obtained results by using variant examples for FZ-simulation functions and admissible mappings. Some examples are provided to illustrate the usability of our main results.

In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of ρ-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces.

In this paper, we presented some new weaker conditions on the Proinov-type contractions which guarantees that a self-mapping T has a unique fixed point in terms of rational forms. Our main results improved the conclusions provided by Andreea Fulga (On (ψ,φ)−Rational Contractions) in which the continuity assumption can either be reduced to orbital continuity, k−continuity, continuity of Tk, T-orbital lower semi-continuity or even it can be removed. Meanwhile, the assumption of monotonicity on auxiliary functions is also removed from our main results. Moreover, based on the obtained fixed point results and the property of symmetry, we propose several Proinov-type contractions for a pair of self-mappings (P,Q) which will ensure the existence of the unique common fixed point of a pair of self-mappings (P,Q). Finally, we obtained some results related to fixed figures such as fixed circles or fixed discs which are symmetrical under the effect of self mappings on metric spaces, we proposed some new types of (ψ,φ)c−rational contractions and obtained the corresponding fixed figure theorems on metric spaces. Several examples are provided to indicate the validity of the results presented.

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

Diaphyseal cross-sectional geometry (CSG) is an effective indicator of humeral bilateral asymmetry. However, previous studies primarily focused on CSG properties from limited locations to represent the overall bilateral biomechanical performance of humeral diaphysis. In this study, the complete humeral diaphyses of 40 pairs of humeri from three Chinese archaeological populations were scanned using high-resolution micro-CT, and their biomechanical asymmetries were quantified by morphometric mapping. Patterns of humeral asymmetry were compared between sub-groups defined by sex and population, and the representativeness of torsional rigidity asymmetry at the 35% and 50% cross-sections (J35 and J50 asymmetry) was testified. Inter-group differences were observed on the mean morphometric maps, but were not statistically significant. Analogous distribution patterns of highly asymmetrical regions, which correspond to major muscle attachments, were observed across nearly all the sexes and populations. The diaphyseal regions with high variability of bilateral asymmetry tended to present a low asymmetrical level. The J35 and J50 asymmetry were related to the overall humeral asymmetry, but the correlation was moderate and they could not reflect localized asymmetrical features across the diaphysis. This study suggests that the overall asymmetry pattern of humeral diaphysis is more complicated than previously revealed by individual sections.

We study the existence and uniqueness of common coupled fixed point of four self-mappings for Geraghty-type contraction using weakly compatible mappings in partially ordered metric spaces with common limit range property (denoted by (CLRST)), the property of E.A, and so on. It is noted that the continuity of mappings and completeness of spaces can be removed. Our results improve, extend, complement, and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.

Our purpose in this paper is to extend the fixed point results of a ψ F -contraction introduced by Secelean N.A. and Wardowski D. ( ψ F -Contractions: Not Necessarily Nonexpansive Picard Operators, Results. Math.70(3), 415−431 (2016)) defined on a metric space X into itself to the case of mapping defined on the product space X I , where I is a set of positive integers (natural numbers). Some improvements to the conditions imposed on function F and space X are provided. An illustrative example is given.

Power sector is significantly important for China to achieve the CO2 emission reduction targets. In this study, we analyze the features of CO2 emissions and environment effect in China’s power sector, investigate the driving factors of CO2 emission change based on the logarithmic mean Divisia index (LMDI) method, and evaluate the mitigation potential of CO2 emissions in China’s power sector. Results show that CO2 emissions in China’s power sector increased rapidly from 492.00 Mt in 1990 to 3049.88 Mt in 2014 while CO2 emission intensity experienced an unsteady downward trend during the study period. Industrial scale effect is the key contributor to CO2 emission growth in China’s power sector, and its contribution degree reaches 123.97%. Energy intensity effect contributes most to the decrease in CO2 emissions, with a contribution degree of −20.01%. Capital productivity effect is another important factor leading to CO2 emissions increase. The aggregate CO2 emission reduction would reach 17973.86 million tons (Mt) during 2015–2030 in the ideal emission reduction scenario. Finally, policy recommendations are made for future energy-saving and CO2 emission reduction in China’s power sector.

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S4PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons are max′-controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S4PR is established.

The main aim of this paper is to establish some coupled common fixed point theorems under a Geraghty-type contraction using mixed weakly monotone property in partially ordered S-metric space. Also, we give some sufficient conditions for the uniqueness of a coupled common fixed point. Some examples are provided to demonstrate the validity of our results.

Transferring emergent target tracking data to sinks is a major challenge in the Industrial Internet of Things (IIoT), because inefficient data transmission can cause significant personnel and property loss. For tracking a constantly moving mobile target, sensing data should be delivered to sinks continuously and quickly. Although there is some related research, the end to end tracking delay is still unsatisfying. In this paper, we propose a Fast and Efficient Data Forwarding (FEDF) scheme for tracking mobile targets in sensor networks to reduce tracking delay and maintain a long lifetime. Innovations of the FEDF scheme that differ from traditional scheme are as follows: firstly, we propose a scheme to transmit sensing data through a Quickly Reacted Routing (QRR) path which can reduce delay efficiently. Duty cycles of most nodes on a QRR path are set to 1, so that sleep delay of most nodes turn 0. In this way, end to end delay can be reduced significantly. Secondly, we propose a perfect method to build QRR path and optimize it, which can make QRR path work more efficiently. Target sensing data routing scheme in this paper belongs to a kind of trail-based routing scheme, so as the target moves, the routing path becomes increasingly long, reducing the working efficiency. We propose a QRR path optimization algorithm, in which the ratio of the routing path length to the optimal path is maintained at a smaller constant in the worst case. Thirdly, it has a long lifetime. In FEDF scheme duty cycles of nodes near sink in a QRR path are the same as that in traditional scheme, but duty cycles of nodes in an energy-rich area are 1. Therefore, not only is the rest energy of network fully made use of, but also the network lifetime stays relatively long. Finally, comprehensive performance analysis shows that the FEDF scheme can realize an optimal end to end delay and energy utilization at the same time, reduce end to end delay by 87.4%, improve network energy utilization by 2.65%, and ensure that network lifetime is not less than previous research.

Karst aquifers are known for their heterogeneous physical properties and irregular complex flow patterns which make it a challenge to describe the hydrological behavior and to quantitatively define the distribution of river flow components using hydrologic models. In this paper, a conceptual lumped hydrologic model, Xin’anjiang model (XAJ), was applied in Sancha River, which is a karst basin in southwest China, for the simulation of streamflow. The performance of XAJ model was evaluated based on the model’s ability to reproduce the streamflow and baseflow. Percentage of bias (PBIAS), Nash-Sutcliffe efficiency (NSE), coefficient of determination (R2), and standard deviation (RSR) were calculated between the simulated and measured flow for both calibration and validation period. The low PBIAS and RSR (2.7% and 0.367 for calibration period, 1.3% and 0.376 for validation period) and the high NSE and R2 (0.866 and 0.866 for calibration period, 0.858 and 0.860 for validation period) indicate that the model structure and parameters are of reasonable validity. Furthermore, streamflow was separated to baseflow and surface flow using the “baseflow programme,” and the calculated results indicate that the model could also reproduce the response of baseflow in such karst system.