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In this paper, we introduce a modified Tseng's extragradient method with a new step-length rule to solve pseudo-monotone variational inequalities in real Hilbert spaces. Under suitable conditions, the sequence generated by this algorithm strongly converges to the common elements of the solution set of pseudo-monotone variational inequality problems and the fixed point set of k-demicontractive mappings. Finally, we give some numerical experiments to illustrate the effectiveness of the proposed algorithm. The main results of this paper generalize and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

The objective of this research is to present a novel approach to enhance the extragradient algorithm's efficiency for finding an element within a set of fixed points of nonexpansive mapping and the set of solutions for equilibrium problems. Specifically, we focus on applications involving a pseudomonotone, Lipschitz-type continuous bifunction. Our main contribution lies in establishing a strong convergence theorem for this method, without relying on the assumption of lim n → ∞ ∥ x n + 1 − x n ∥ = 0 . Moreover, the main theorem can be applied to effectively solve the combination of variational inequality problem (CVIP). In support of our main result, numerical examples are also presented. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some fixed point results in the setting of metric-like space by defining an (α, β)-admissible z-contraction mapping imbedded in simulation function. Our results generalize and extend several well known results in the literature of fixed point theory. A suitable example is also established to verify the validity of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the novel concept of generalized distance denoted as J θ and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance J θ (u , H ★) , a generalized Hausdorff type distance and a P J θ -property of a pair (H ★ , K ★) of nonempty subsets of extended b-metric space (U ★ , ρ θ). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples. [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 introduce two types of weak enriched contractions, namely weak enriched F -contraction, weak enriched F ′ -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 FROM AUTHOR]

In this paper, we propose a strongly convergent simultaneous cutter method for finding the minimal norm solution over the intersection of fixed point sets of cutters. The proposed method is the combination of the simultaneous cutter method and the strongly variance of Krasnosel'skiĭ-Mann method. We show a strong convergence result of the sequence generated by the proposed method to the unique minimal norm solution. We finally present the numerical experiments on the minimal norm solution over a finite number of linear feasibility problem. [ABSTRACT FROM AUTHOR]

In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and zero points of maximal monotone mapping in reflexive Banach space. Using this result, we get a new strong convergence theorem in Banach space. Our result extends and improves important recent results presented by many authors. [ABSTRACT FROM AUTHOR]

We present enriched Kannan and enriched Bianchini mappings in the framework of unique geodesic spaces. For such mappings, we establish the existence and uniqueness of a fixed point in the setting of CAT(0) spaces and show that an appropriate Krasnoselskij scheme converges with certain rate to the fixed point. We proved some inclusion relations between enriched Kannan mapping and some applicable mappings such as strongly demicontractive mapping. Finally, we give an example in a nonlinear CAT(0) space and perform numerical experiments to support the theoretical results. [ABSTRACT FROM AUTHOR]

Our goal of this paper is to solve the problem of common fixed point of a quite large family of demiclosed cutters on Hilbert spaces. We introduce two new extrapolated simultaneous block‐iterative methods. The first method converges weakly to a common fixed point of the family and the second one is a specific combination of the first and the steepest descent method and converges in norm. Its strong convergence is proved without additional conditions on the cutters such as the approximately shrinking property of each cutter and bounded regular assumption on their fixed point sets, assumed recently in the literature. Some particular cases of the last method, applications and computational experiments to a convex optimization over the intersection of level sets are given for illustration and comparison. [ABSTRACT FROM AUTHOR]

In this manuscript, our objective is to introduce the notion of neutrosophic extended metric-like spaces. We establish some fixed point theorems in this setting. Neutrosophic extended metric-like spaces metric space uses the idea of continuous triangular norms and continuous triangular conorms in an extended intuitionistic fuzzy metric-like space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. Triangular norms and triangular conorm are very significant for fuzzy operation. The obtained results boost the approaches of existing ones in the literature and are supported by some examples and an application. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find a common element of the fixed point set of a nonexpansive mapping and the set of solutions of the general split variational inclusion problem in symmetric Hilbert spaces by using the inertial viscosity iterative method. Some strong convergence theorems of the proposed algorithm are demonstrated. As applications, we use our results to study the split feasibility problem and the split minimization problem. Finally, the numerical experiments are presented to illustrate the feasibility and effectiveness of our theoretical findings, and our results extend and improve many recent ones. [ABSTRACT FROM AUTHOR]

From the moment when the concept of the orthogonal set appeared in 2017, it become an interesting topic for research. Many authors investigated the uniqueness of best proximal point results in different types of metric space (X, d) where X is an orthogonal set and d is a metric on X. Investigation of those results goes in two main directions. The first type of investigation direction deals with different metric spaces, such as standard metric space, b-metric spaces, metric-like spaces, b metric-like spaces, modular spaces, etc. The second direction deals with different types of contraction. Firstly, we present some necessary definitions with many examples for a better understanding of the concept of the orthogonal set. After that, we give an overview of some results in this field and open problems that could be considered. [ABSTRACT FROM AUTHOR]

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched ρ -contractions and enriched ρ -Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched ρ -contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched ρ -contractions. We make a first ever attempt to prove existence results for enriched ρ -Kannan mappings and deduce the result for ρ -Kannan mappings. Note that even ρ -Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples. [ABSTRACT FROM AUTHOR]

In this paper we introduce multivalued modified F-contraction on a metric space. This is a multivalued mapping obtained by incorporating the idea of the recently introduced F-contraction which has attracted much attention in contemporary research. We explore the fixed point problem associated with the above contractive mapping. We also investigate the data dependence and stability properties of the fixed point sets associated with these multival- ued contractions. We discuss an illustration of the main result and present an application of the single valued version of the main theorem to a problem of an integral equation of Volterra type. The domain of the study is fixed point theory and set valued analysis. [ABSTRACT FROM AUTHOR]

The fixed-circle issue is a geometric technique that is connected to the study of geometric characteristics of certain points, and that are fixed by the self-mapping of either the metric space or of the generalized space. The fixed-disc problem is a natural resultant that arises as a direct outcome of this problem. In this study, our goal is to examine new classes of self-mappings that meet a new particular sort of contraction in a metric space. The common geometrical characteristic of the set of fixed points of any element of these classes is that a circle or even a disc, that is either termed the fixed circle or even the fixed disc of the appropriate self-map, is included within that set. In order to accomplish this, we establish two new classifications of contraction mapping: F c -contractive mapping and F c -expanding mapping. In the investigation of neural networks, activation functions with either fixed circles (or even fixed discs) are observed frequently. This demonstrates how successful our results with the fixed-circle (respectively, the fixed-disc) model were. [ABSTRACT FROM AUTHOR]

In this manuscript, our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces. We establish some fixed point theorems in this setting. Also, we plot some graphs of an example of obtained result for better understanding. We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. The obtained results boost the approaches of existing ones in the literature and are supported by some examples and applications. [ABSTRACT FROM AUTHOR]

Novel cyclic contractions of the Kannan and Chatterjea type are presented in this study. With the aid of these brand-new contractions, new results for the existence and uniqueness of fixed points in the setting of complete generalized metric space have been established. Importantly, the results are generalizations and extensions of fixed point theorems by Chatterjea and Kannan and their cyclical expansions that are found in the literature. Additionally, several of the existing results on fixed points in generalized metric space will be generalized by the results presented in this work. Interestingly, the findings have a variety of applications in engineering and sciences. Examples have been given at the end to show the reliability of the demonstrated results. [ABSTRACT FROM AUTHOR]

We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish ∆ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems. [ABSTRACT FROM AUTHOR]

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

In this paper, for solving the variational inequality problem over the set of common fixed points of a finite family of demiclosed quasi-nonexpansive mappings in Hilbert spaces, we propose two new strongly convergent methods, constructed by specific combinations between the steepest-descent method and the block-iterative ones. The strong convergence is proved without the boundedly regular assumptions on the family of fixed point sets as well as the approximately shrinking property for each mapping of the family, that are usually assumed in recent literature for similar problems. Applications to the multiple-operator split common fixed point problem (MOSCFPP) and the problem of common minimum points of a finite family of lower semi-continuous convex functions with numerical experiments are given. [ABSTRACT FROM AUTHOR]

In 2020, Niu et al. [Cryptogr. Commun., 2020, 12(2): 165–185] studied the fixed points of involutions over the finite field with q-elements. This paper further discusses the relationship between the fixed points set and the non-fixed points set of two involutions f1(x) and f2(x) over the finite field F q , and then obtains a necessary and sufficient condition for that the composite function f1 ∘ f2(x) is also an involution over F q . In particular, a special class of involutions over some finite fields is determined completely. [ABSTRACT FROM AUTHOR]

In this paper, we consider a quadratic non-stochastic operator mapping two-dimensional (2D) simplex to itself. We find all fixed points and invariant sets of the operator. Moreover, we study behavior of trajectories generated by the operator. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of Perov–Ćirić–Prešić-type Θ -contractions and to obtain some generalized fixed point theorems in the setting of vector-valued metric spaces. We derive some fixed point results as consequences of our main results. A nontrivial example is also provided to support the validity of our established results. As an application, we investigate the solution of a semilinear operator system in Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we introduced the concept of derivation on equality algebra E by using the notions of inner and outer derivations. Then, we investigated some properties of (inner, outer) derivation and we introduced some suitable conditions that they help us to define a derivation on E . We introduced kernel and fixed point sets of derivation on E and prove that under which condition they are filters of E . Finally, we prove that the equivalence relations on (E , ⇝ , 1) coincide with the equivalence relations on E with derivation d . [ABSTRACT FROM AUTHOR]

We consider a population consisting of two species whose dynamics is determined by a quadratic stochastic operator with variable coefficients, which makes it a discontinuous operator at two points. This operator depends on three parameters. The set of these parameters is divided into seven subsets. For each subset of parameters, we find fixed points, periodic points, and the set of limit points of trajectories generated by the respective quadratic stochastic operators. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce generalized hybrid mappings in hyperbolic metric spaces. We first show that the set of fixed points of such mappings is closed and convex. We then prove the existence of fixed point of these mappings and fi nally approximate th e fix ed poi nt usi ng Mann iterative process. We have also provided an example of generalized hybrid mappings in the setting of -trees for the first time in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct some designs invariant under the alternating groups, using a method that has been recently introduced by Moori. We consider the action of An on the 2-subsets of a set of size n. The blocks of the designs are the conjugates of the set of fixed-points of the permutation with respect to this action. For every element g ∈ A n , we give explicit formulae to compute the parameters of the designs based on the cycle representation of g. We also prove that the binary codes of these designs have minimum distances at most 4. [ABSTRACT FROM AUTHOR]

In our 2014 work with M. Gabour, we introduced a metric space of generalized nonexpansive self-mappings of bounded and closed subsets of a Banach space and studied, using the Baire category approach, the asymptotic behavior of iterates of a generic operator belonging to this class. In the definition of a generalized nonexpansive mapping the norm is replaced by a general function which can be symmetric as a particular case. In this paper, we prove the convergence of infinite products of generalized nonexpansive self-mappings to a common fixed point in a generic setting. [ABSTRACT FROM AUTHOR]

In this paper, we study the class of cyclic contractions in the setting of S-metric spaces involving C-class function and establish some fixed point theorems in the setting of complete S-metric spaces. We support our results with some examples. Our results extend and generalize several results from the existing literature (see, e.g., [3, 8, 9, 14, 15, 20] and many others) to the case of more general ambient space and contraction condition. [ABSTRACT FROM AUTHOR]

The purpose of this article is to prove some unique fixed point theorems in the setting of S-metric spaces via simulation functions. We give some examples in support of our results and also some consequences of our result. This work extend and generalize some results in the existing literature. [ABSTRACT FROM AUTHOR]

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We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties to the componental operators rather than to the full operators. The operatorial properties that we discuss include nonexpansivity, firm nonexpansivity, relaxed firm nonexpansivity, averagedness, being a cutter, quasi-nonexpansivity, strong quasi-nonexpansivity, strict quasi-nonexpansivity and contraction. Some relationships between operators whose componental operators have such properties and operators that have these properties on the product space are studied. This enables also to define componental fixed point sets and to study their properties. For componental contractions we offer a variant of the Banach fixed point theorem. Our motivation comes from the desire to extend a fully-simultaneous method that takes into account sparsity of the linear system in order to accelerate convergence. This was originally applicable to the linear case only and gives rise to an iterative process that uses different componental operators during iterations. [ABSTRACT FROM AUTHOR]

Assume that ρ is a convex modular satisfying the Δ 2 -type condition and the modular space is either α-uniformly ρ-noncompact convex or it satisfies the strong Opial condition. We prove that the fixed point set of a commuting family of asymptotically non-expansive mappings defined from a ρ-convex weakly compact set C into C is a non-empty nonexpansive retract of C. We show that our results about existence of fixed point for commuting families of nonexpansive mappings also work if we replace the weak topology by some other topologies weaker than the ρ-topology. In particular, we can obtain fixed point results when C is ρ-a.e. compact in a modular function space. [ABSTRACT FROM AUTHOR]

Motivated by the China's five element philosophy (CFEP), we construct a permuted Volterra quadratic stochastic operator acting on the four-dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution operator for CFEP. We study the discrete-time dynamical system generated by this operator. Mainly our results related to a symmetric operator (depending on one parameter). We show that this operator has a unique fixed point, which is repeller. Moreover, in the case of non-zero parameter, it has two 5-periodic orbits. We divide the simplex to four subsets: the first set consists a single point (the fixed point); the second (resp. third) set is the set of initial point trajectories of which converge to the first (resp. second) 5-periodic orbit; the fourth subset is the set of initial point trajectories of which do not converge and their sets of limit points are infinite and lie on the boundary of the simplex. We give interpretations of our results to CFEP. [ABSTRACT FROM AUTHOR]

In this manuscript we introduce the notion of (α , β , ψ , ϕ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings. [ABSTRACT FROM AUTHOR]

This article, dedicated to Mahlon M. Day, introduces free group presentations of planar vortexes in a CW space that are a natural outcome of results for amenable groups and fixed points found by M.M. Day during the 1960s and a fundamental result for fixed points given by L.E.J. Brouwer. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of generalized asymmetric metric spaces and we prove some fixed point theorems in the setting of this metric spaces and also some illustrative examples are given. The presented results generalize and improve several results of the topics in the literature. [ABSTRACT FROM AUTHOR]

Let (X, ||⋅||) be a normed linear space. Let K be a nonempty closed convex subset of X. Let T : K → K be a contractive-like operator with a nonempty fixed point set F(T). We prove the strong convergence and T-stability of Picard S-iteration procedure with respect to the contractive-like operator T which are independent for any arbitrary choices of the sequences [αn}n=0∞ and [βn}n=0∞ in [0,1]. [ABSTRACT FROM AUTHOR]

In this paper, we develop an iterative algorithm for obtaining common so- lutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a new viscosity iterative algorithm for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping and the set of solutions of a new variational inequality problem involving inverse-strongly monotone operators in Hilbert spaces. We prove some strong convergence theorems under some suitable assumptions imposed on the parameters by using a modified extragradient method. The results obtained in this paper may be an improvement of many recent ones in this fields. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and Δ-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed. [ABSTRACT FROM AUTHOR]

Let (M,d) be a metric space, X⊂ M be a nonempty closed subset and K⊂ M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F:X→ P(X) is said to be a strong Frum-Ketkov type operator if there exists α ∈ ]0,1[ such that ed(F(x),K)\≤ α Dd(x,K), for every x→ X, where ed is the excess functional generated by d and Dd is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators. [ABSTRACT FROM AUTHOR]

This paper proposes a stochastic approximation method for solving a convex stochastic optimization problem over the fixed point set of a quasinonexpansive mapping. The proposed method is based on the existing adaptive learning rate optimization algorithms that use certain diagonal positive-definite matrices for training deep neural networks. This paper includes convergence analyses and convergence rate analyses for the proposed method under specific assumptions. Results show that any accumulation point of the sequence generated by the method with diminishing step-sizes almost surely belongs to the solution set of a stochastic optimization problem in deep learning. Additionally, we apply the learning methods based on the existing and proposed methods to classifier ensemble problems and conduct a numerical performance comparison showing that the proposed learning methods achieve high accuracies faster than the existing learning method. [ABSTRACT FROM AUTHOR]

In this paper we give some theorems of existence of best points of proximity for a multifunctional non-self-mapping in a partial metric space and some approximations on the sets of the best points of proximity. Other results are also given. [ABSTRACT FROM AUTHOR]

It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point x to the set of fixed points of a set-valued contraction mapping Φ is bounded by a constant times the distance from x to Φ(x). In this paper, we generalize both this result and Lim's lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of (ff;)-rational type contrac- tive mappings to prove some unique fixed point theorems in the setting of rectangular b-metric space. We deduce some results as corollaries and exam- ples are also given to verify the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi's viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze the convergence of new iteration methods for finding a common point of the solution set of a class of pseudomonotone variational inequalities and the fixed point set of a finite system of nonexpansive mappings in a real Hilbert space. The idea of this algorithm is to combine the subgradient method with the parallel splitting-up techniques. The main iteration step in the proposed methods uses only one projection and does not require any Lipschitz continuous condition for the cost mapping. The convergent results are also extended to a pseudomonotone equilibrium problem involving a finite system of nonexpansive mappings. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms. [ABSTRACT FROM AUTHOR]