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The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via φ-contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested. [ABSTRACT FROM AUTHOR]

We construct a counterexample that disproves the claim of Theorem 0.2 of the paper “Injective mappings and solvable vector fields of Euclidean spaces”, which appeared in Topology Appl. 136 (2004), 261–274. [ABSTRACT FROM AUTHOR]

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

Bibliometric analysis is the quantitative study of bibliographic material. In this paper, a systematic review of papers, authors, and journals is carried out. This is necessary to determine and set targets to be achieved in further research. The main objective of this study is to identify some of the most relevant research and the latest trends according to the information found in the Google Scholar, Publish or Perish, Science Direct, and Dimension databases. The methods used are classification, analysis of the most cited journals of all time, and the most prolific and influential authors. The results are information on the number of papers, citations, researchers, h-index, g-index, major reference journals, and visualization of research roadmaps for the topic of agricultural insurance mathematical models. The research findings identify the core themes, which are used as research gaps for future research. [ABSTRACT FROM AUTHOR]

This paper delves into fixed point findings within a complete partially ordered b-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of mixed (S,T)-α-admissible mappings and interspersed (S, g,T)-α-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized (αs, ξ, ħ, τ)-Geraghty contractive mapping in the framework of partial b-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results. [ABSTRACT FROM AUTHOR]

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. [ABSTRACT FROM AUTHOR]

Achieving scientific document retrieval by considering the wealth of mathematical expressions and the semantic text they contain has become an inescapable trend. Current scientific document matching models focus solely on the textual features of expressions and frequently encounter hurdles like proliferative parameters and sluggish reasoning speeds in the pursuit of improved performance. To solve this problem, this paper proposes a scientific document retrieval method founded upon hesitant fuzzy sets (HFS) and local semantic distillation (LSD). Concretely, in order to extract both spatial and semantic features for each symbol within a mathematical expression, this paper introduces an expression analysis module that leverages HFS to establish feature indices. Secondly, to enhance contextual semantic alignment, the method of knowledge distillation is employed to refine the pretrained language model and establish a twin network for semantic matching. Lastly, by amalgamating mathematical expressions with contextual semantic features, the retrieval results can be made more efficient and rational. Experiments were implemented on the NTCIR dataset and the expanded Chinese dataset. The average MAP for mathematical expression retrieval results was 83.0%, and the average nDCG for sorting scientific documents was 85.8%. [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 new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of mappings with bounded and finite distortion defined in some domain of the Euclidean space. We consider mappings that satisfy some upper estimates for the distortion of the modulus of families of paths, where the order of the modulus equals to p, n - 1 < p ⩽ n. The main problem studied in the manuscript is the investigation of the boundary behavior of such mappings, more precisely, the distortion of the distance under mappings near boundary points. The publication is primarily devoted to definition domains with "bad boundaries", in which the mappings not even have a continuous extension to the boundary in the Euclidean sense. However, we introduce the concept of a quasiconformal regular domain in which the specified continuous extension is valid and the corresponding distance distortion estimates are satisfied; however, both must be understood in the sense of the socalled prime ends. More precisely, such estimates hold in the case when the mapping acts from a quasiconformal regular domain to an Ahlfors regular domain with the Poincar'e inequality. The consideration of domains that are Ahlfors regular and satisfy the Poincar'e inequality is due to the fact that, lower estimates for the modulus of families of paths through the diameter of the corresponding sets hold in these domains. (There are the so-called Loewner-type estimates). We consider homeomorphisms and mappings with branching separately. The main analytical condition under which the results of the paper were obtained is the finiteness of the integral averages of some majorant involved in the defining modulus inequality under infinitesimal balls. This condition includes the situation of quasiconformal and quasiregular mappings, because for them the specified majorant is itself bounded in a definition domain. Also, the results of the article are valid for more general classes for which Poletsky-type upper moduli inequalities are satisfied, for example, for mappings with finite length distortion. [ABSTRACT FROM AUTHOR]

We explore the intermixed method for finding a common element of the intersection of the solution set of a mixed variational inequality and the fixed point set of a nonexpansive mapping. We point out that Khuangsatung and Kangtunyakarn's statement [J. Inequal. Appl. 2023:1, 2023] regarding the resolvent utilized in their paper is not correct. To resolve this gap, we employ the epigraphical projection and the product space approach. In particular, we obtain a strong convergence theorem with a weaker assumption. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of (incident) higher-order generalized epiderivative for a set-valued map and obtain a crucial result of the epiderivative. Then we use this result to establish the higher-order sufficient and necessary optimality conditions of a constrained set-valued optimization problem. By virtue of the epiderivatives and the optimality conditions, we establish the higher-order mixed duality problem for the set-valued optimization problem and obtain the corresponding duality theorems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a faster iterative method for approximating the fixed points of generalized α -nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results. [ABSTRACT FROM AUTHOR]

This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, Hölder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples. [ABSTRACT FROM AUTHOR]

In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors between this category and the categories Pos-S of all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study the existence of their left and right adjoints. It is shown that the category Pos-S is a full reflective and coreflective subcategory of PosAct-S. [ABSTRACT FROM AUTHOR]

In the paper we study equiaffine immersions f: (Mn,∇) → Rn+2 with flat connection ∇ and one-dimensional Weingarten mapping. For such immersions there are two types of the transversal distribution equiaffine frame. We give a parametrization of a submanifold with the given properties for both types of equiaffine frame. The main result of the paper is contained in Theorems 1, 2 and Corollary 1: Let f: (Mn,∇) → (Rn+2,D) be an affine immersion with pointwise codimension 2, equiaffine structure, flat connection ∇, one-dimensional Weingarten mapping then there exists three types of its parametrization: (i)→r = g(u¹, . . ., un)→a1 + R→φ(u¹)du¹ + nΣi=2 ui→ai; (ii)→r = (g(u², . . ., un) + u¹)→a + ∫v(u¹)→η(u1)du¹ + Σni=2 ui ∫ λi(u¹)→η(u¹)du¹; (iii)→r = (g(u², . . ., un) + u¹)→ρ(u¹) + ∫ (v(u¹) - u¹) d→ρ(u¹)/du¹du¹ + Σni=2 ui ∫ λi(u¹) d→ρ(u¹). du¹du1. [ABSTRACT FROM AUTHOR]

Big data (BD) is one of the emerging topics in the field of information systems. This article utilized citation and co-citation analysis to explore research articles in the field of BD to examine the scientific development in the area. The research data was retrieved from the WOS database from the period between 2005 and June 2016, which consists of 366 articles. In the citation analysis, this article relies on the degree centrality and betweenness centrality for identifying 38 important papers in BD. In the co-citation analysis, a principal component factor analysis of the co-citation matrix is employed for identifying six major research themes: foundations, BD applications, techniques and technologies, challenges, adoption and impacts and literature review. This literature review is one of the first studies to examine the knowledge structure of BD research in the information systems discipline by using evidence-based analysis methods. Recommendations for future research directions in BD are provided based on the analysis and results of this study. [ABSTRACT FROM AUTHOR]

In this paper, we introduce triple θ-centralizers and weak triple θ-centralizers on an algebra A, where θ: A → A is a triple homomorphism. Some observations concerning triple θ-centralizers, weak triple θ-centralizers and approximate weak triple θ-centralizers are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions. The backward recurrence algorithm is one of the basic tools of computation approximants of branched continued fractions. Like most recursive processes, it is susceptible to error growth. Each cycle of the recursive process not only generates its own rounding errors but also inherits the rounding errors committed in all the previous cycles. On the other hand, in general, branched continued fractions are a non-linear object of study (the sum of two fractional-linear mappings is not always a fractional-linear mapping). In this work, we are dealing with a confluent branched continued fraction, which is a continued fraction in its form. The essential difference here is that the approximants of the continued fraction are the so-called figure approximants of the branched continued fraction. An estimate of the relative rounding error, produced by the backward recurrence algorithm in calculating an nth approximant of the branched continued fraction expansion of Horn's hypergeometric function H4, is established. The derivation uses the methods of the theory of branched continued fractions, which are essential in developing convergence criteria. The numerical examples illustrate the numerical stability of the backward recurrence algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and uniqueness of solutions for the following nonlinear multi-order fractional differential equation with integral boundary conditions { (C D 0 + α u) (t) + ∑ i = 1 m λ i (t) (C D 0 + α i u) (t) + ∑ j = 1 n μ j (t) (C D 0 + β j u) (t) + ∑ k = 1 p ξ k (t) (C D 0 + γ k u) (t) + ∑ l = 1 q ω l (t) (C D 0 + δ l u) (t) + σ (t) u (t) + f (t , u (t)) = 0 , t ∈ [ 0 , 1 ] , u ″ (0) = u ‴ (0) = 0 , u ′ (0) = η 1 ∫ 0 1 u (s) d s , u (1) = η 2 ∫ 0 1 u (s) d s , where 0 < δ 1 < δ 2 < ⋯ < δ q < 1 < γ 1 < γ 2 < ⋯ < γ p < 2 < β 1 < β 2 < ⋯ < β n < 3 < α 1 < α 2 < ⋯ < α m < α < 4 and η 1 + 2 (1 − η 2) ≠ 0 . Using a fixed point theorem and Banach contractive mapping principle, we obtain some existence and uniqueness results. [ABSTRACT FROM AUTHOR]

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some common fixed point theorems for two pairs of self-mappings satisfying (CLR)-property and some Φ-type contractive condition in the framework of S-metric spaces. We also give some examples to validate the results. The results presented in this paper generalize, extend and unify several previous results in the existing literature. [ABSTRACT FROM AUTHOR]

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method's efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. [ABSTRACT FROM AUTHOR]

In the context of uniformly convex Banach space, this paper focuses on examining the strong convergence of the F * iterative algorithm to the fixed point of a strongly pseudocontractive mapping. Furthermore, we demonstrate through numerical methods that the F * iterative algorithm converges strongly and faster than other current iterative schemes in the literature and extends to the fixed point of a strong pseudocontractive mapping. Finally, under a nonlinear quadratic Volterra integral equation, the application of our findings is shown. [ABSTRACT FROM AUTHOR]

In the paper, nonlinear vibration characteristics of a rotor system are investigated. Such a nonlinear rotor system is subjected to brush seal forces, which are obtained by integrating the bristle force along the entire ring. The nonlinear brush seal rotor system is constructed by merging a flexible rotor with nonlinear seal forces. The research is aimed at studying the nonlinear vibration characteristics and bifurcations of the motions under a variety of eccentricity circumstances. Different kinds of bifurcations are successfully obtained by mathematical discretization and mapping manipulation. Such a discrete mapping method successfully predicts the stable and unstable motions accurately. The period-doubling bifurcations and saddle node bifurcations of the rotor system are obtained. The sole unstable solutions are obtained, which are special, and a normal numerical integration method cannot solve this problem, which provides advantages in rotor design and motion control. According to the results, nonlinear resonances are found between the stable and unstable motions. The greater the eccentricity of the rotor, the greater the number of bifurcation points that occur during the rotor's nonlinear motions, as well as the larger the ranges of speeds where the motions are unstable. Saddle node bifurcations generate unstable nonlinear motions and non-smooth motions, which may bring damage to the mechanical rotors. The period-doubling bifurcations produce the route from period-1 to period-2 motions in the nonlinear rotor system. The research provides a new perspective to study the bifurcations and stability of the nonlinear rotor systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new hybrid relaxed iterative algorithm with two half-spaces to solve the fixed-point problem and split-feasibility problem involving demicontractive mappings. The strong convergence of the iterative sequence produced by our algorithm is proved under certain weak conditions. We give several numerical experiments to demonstrate the efficiency of the proposed iterative method in comparison with previous algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a common fixed point result in Menger space in two pairs and three pairs of self mappings by using occasionally weakly compatible mappings. Our first theorem generalizes the theorem of Sharma and Shahu [1] and B. Fisher et al. [2] and both theorems deduce some similar results in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to establish some results on the structure of fixed point sets for mappings in 2-inner product spaces. To this end, we employ some well-known techniques of 2-inner product spaces. [ABSTRACT FROM AUTHOR]

This work focuses on quasi efficient solutions of a vector optimization problem. Namely, it is assumed the objective function to map values between finite dimensional spaces and the ordering in the final space is defined by a pointed convex cone. In this setting, several new concepts of quasi efficient solutions are introduced and their basic properties are obtained. After that, it is studied their limit behavior in order to deduce when they approximate well other kind of efficient solutions of the problem. Finally, in convex problems, linear scalarization results are stated that relate the introduced quasi efficient solutions with solutions of scalar optimization problems. The concepts and results of the paper extend and clarify several ones of the recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to study set-valued discrete dynamical systems with the objective of developing a general framework and unifying some results and definitions in the literature. For these purposes, we follow similar ideas to those existing for classical dynamical systems. We focus on discrete dynamical systems in terms of set-valued maps. The solutions associated to our systems are given by sequences of sets. We obtain preliminary results by formulating appropriate notions of set dynamical systems as attractor, stability and invariant sets. For this purpose, we study the ω-limit sets which play an important role for gaining an overall understanding of how the system is behaving, particularly in the long term. We study its properties by using well-known notions from set-valued analysis. We are able to generalize dynamical results in terms of single valued maps by the weaker assumptions on continuity. [ABSTRACT FROM AUTHOR]

In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by Zµ- contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results. [ABSTRACT FROM AUTHOR]

Ecosystems provide various goods and services to society and their valuation is among the main objectives of the concept of ecosystem services (ES). The mapping of ecosystems is the main building block of the whole process of the Mapping and Assessment of Ecosystems and their Services (MAES). The analyses of the ecosystem data produced during the implementation of the national methodology for mapping ecosystems in Bulgaria (MAES BG) reveal some problems that may cause confusion in cases of integrated assessment of all ecosystem types. In this paper, we present an approach that enables formulation of a uniform spatial dataset based on the mapping of the main ecosystem types, that can be used for mapping of ES at a river basin scale. It has been applied to the upper part of the Ogosta River basin and the result is a topologically correct uniform spatial data layer. The approach gives one possible solution to problems related to the different sources of information and the discrepancies between ecosystem types in the national mapping of ecosystems in Bulgaria. It is based on the use of a uniform spatial framework that outlines the ecosystem types and sets the initial database for further mapping. This ensures a topologically correct spatial dataset for the ecosystems and a background for further updates for each ecosystem at the different levels of MAES typology. The most appropriate spatial basis for the territory of Bulgaria is the database for the physical blocks of the Ministry of Interior. Its application to the studied river basin gives encouraging results and can be used as an example for similar areas. Further development of the approach will ensure the mapping of the forest ecosystems at level 3 of the MAES BG typology and more precise delineation of the grassland, heathland, freshwater, and sparsely vegetated ecosystems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the oscillatory behaviour of a class of first-order sublinear and superlinear neutral difference equations. Some conditions are established by applying Banach's Contraction mapping principle, Knaster-Tarski fixed point theorem and using several inequalities. We provide some examples to illustrate the outreach of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial value problem for a semi-linear heat equation with memory in n-dimensional space Rn. Under a smallness conditions on the initial data, the global existence and decay estimates of the solutions are established. Furthermore, time decay estimates in higher Sobolev space of the solution are provided. The proof is carried out by means of the point-wise decay estimates of the solution in the Fourier space and a fixed point-contraction mapping argument. [ABSTRACT FROM AUTHOR]

In this paper by taking into account three trends, prevalent in metric fixed point theory, namely, use of control functions instead of contraction constants, consideration of relational structure in the metric space and fixed point studies of discontinuous functions, we formulate and solve a new problem in relational metric fixed point theory. Our result extends the well known result of Kannan. The theorems are illustrated with examples. Further the problem is shown to have Hyers-Ulam-Rassias stability property. We make an application of our main result to a problem of a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish weak and strong convergence theorems of new three-step iterations for Iasymptotically nonexpansive mappings in Banach space.Also we introduce and study convergence theorems of the three-step iterative sequence for three I-asymptotically nonexpansive mappings in an uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by Chen and Guo [1], S. Temir [14], Yao and Noor[16] and many others. [ABSTRACT FROM AUTHOR]

While gamification is gaining ground in business, marketing, corporate management, and wellness initiatives, its application in education is still an emerging trend. This article presents a study of the published empirical research on the application of gamification to education. The study is limited to papers that discuss explicitly the effects of using game elements in specific educational contexts. It employs a systematic mapping design. Accordingly, a categorical structure for classifying the research results is proposed based on the extracted topics discussed in the reviewed papers. The categories include gamification design principles, game mechanics, context of applying gamification (type of application, educational level, and academic subject), implementation, and evaluation. By mapping the published works to the classification criteria and analyzing them, the study highlights the directions of the currently conducted empirical research on applying gamification to education. It also indicates some major obstacles and needs, such as the need for proper technological support, for controlled studies demonstrating reliable positive or negative results of using specific game elements in particular educational contexts, etc. Although most of the reviewed papers report promising results, more substantial empirical research is needed to determine whether both extrinsic and intrinsic motivation of the learners can be influenced by gamification. [ABSTRACT FROM AUTHOR]

It is important to cluster heterogeneous information networks. A fast clustering algorithm based on an approximate commute time embedding for heterogeneous information networks with a star network schema is proposed in this paper by utilizing the sparsity of heterogeneous information networks. First, a heterogeneous information network is transformed into multiple compatible bipartite graphs from the compatible point of view. Second, the approximate commute time embedding of each bipartite graph is computed using random mapping and a linear time solver. All of the indicator subsets in each embedding simultaneously determine the target dataset. Finally, a general model is formulated by these indicator subsets, and a fast algorithm is derived by simultaneously clustering all of the indicator subsets using the sum of the weighted distances for all indicators for an identical target object. The proposed fast algorithm, FctClus, is shown to be efficient and generalizable and exhibits high clustering accuracy and fast computation speed based on a theoretic analysis and experimental verification. [ABSTRACT FROM AUTHOR]

This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define a Berinde type ( ρ , μ)- ϑ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

The main aim of this work is to use the XOR-operation technique to find the common solutions for a new class of extended system of fuzzy ordered variational inclusions with its corresponding system of fuzzy ordered resolvent equations involving the operation and fixed point problems, which are slightly different from corresponding problems considered in several recent papers in the literature and are more advantageous. We establish that the system of fuzzy ordered variational inclusions is equivalent to a fixed point problem and a relationship between a system of fuzzy ordered variational inclusions and a system of fuzzy ordered resolvent equations is shown. We prove the existence of a common solution and discuss the convergence of the sequence of iterates generated by the algorithm for a considered problem. The iterative algorithm and results demonstrated in this article have witnessed, a significant improvement for many previously known results of this domain. Some examples are constructed in support of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of neutrosophic pentagonal metric space. We prove several interesting results for some classes contraction mappings and prove some fixed point theorems in neutrosophic pentagonal metric space. Finally, we prove the uniqueness and existence of the integral equation and fractional differential equation to support our main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided. [ABSTRACT FROM AUTHOR]

In the present paper, we prove common fixed point theorems under different contractive mappings on C ★ -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution. [ABSTRACT FROM AUTHOR]

In this paper, an a-complete extended Branciari b-distance space and rational α -- λ -- JS contractive conditions in the underlying spaces are introduced. Further, we establish the coincidence point, common fixed points, and uniqueness of fixed points for two pairs of mappings in new spaces under the aforementioned contractive conditions. We illustrate the work with an example and apply the results to determine the existence of solutions for a system of Urysohn integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove a common fixed-point theorem for four self-mappings with a function family on -metric spaces. In addition, we investigate some geometric properties of the fixed-point set of a given self-mapping. In this context, we obtain a fixed-disc (resp. fixed-circle), fixed-ellipse, fixed-hyperbola, fixed-Cassini curve and fixed-Apollonious circle theorems on -metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we prove that if φ: R → R' is an n-Jordan homomorphism, where R has a unit e, then the map a ↦ φ(e)n-2φ(a) is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each n-Jordan homomorphism is an n-homomorphism. [ABSTRACT FROM AUTHOR]