The purpose of the current article is to review some historical facts about the process of editing Carpathian Journal of Mathematics (CJM) since its foundation in 1991 to the present time (2026) and to reflect systematically on articles recently published in CJM. The bibliometrics analysis was carried out over the past 10 year research activity of the journal, i.e., over the period from 2016 to 2025, and was conducted with the aim to analyze and characterize its most important aspects. The data for the analysis have been obtained and analyzed separately from each of the following databases: MathSciNet, zbMATH, Scopus, and Web of Science. Based on a quantitative content analysis of the journal's articles, the statistical analysis was directed mainly to identify the most contributing authors, organizations, research groups and countries. The analysis also examined the impact and visibility of the publications in CJM based on reviews and citations over the whole publication period of the journal according to information available within the five databases taken into consideration.

Our aim in this paper is to construct four efficient viscosity-type algorithms with certain acceleration techniques for solving a pseudomonotone and Lipschitzian variational inequality problem in conjunction with a common fixed point problem of two demicontractive mappings in infinite-dimensional real Hilbert space. We employ a self-adaptive strategy, which does not require any information on the Lipschitz constant of the operator or a line search procedure, in order to effectively generate a sequence of step lengths in each of the proposed algorithms. Besides some extrapolation techniques in each of the proposed algorithms, the first and third unify two steps of the recent improved versions of the inertial term called alternating and multi-step inertial terms, while the second and fourth integrate the three-term conjugate gradient-like direction and alternating inertial term. These techniques significantly improve the convergence of the suggested algorithms. Under some minimal assumptions, we formulate and prove a strong convergence theorem for each of the algorithms based on convergence of some extrapolated viscosity-type algorithms with alternating inertial terms and perturbations to a common minimum norm solution of the problems in infinite-dimensional real Hilbert spaces. In contrast to some existing conjugate gradient-like algorithms, our proposed three-term conjugate gradient-like algorithms do not require any of the restrictive boundedness assumptions, these make them interesting and simple in this area, which both theoretically and numerically improve their convergence properties. Moreover, we investigate the possible applications of the proposed algorithms in classification problems for some interesting real-world dataset, cybersecurity investments in supply chain networks

In this paper, we present approximation results for a generalized alpha-non-expansive multi-valued mapping using a four-step iteration scheme introduced in the context of a convex metric space. We extend some recent results about generalized alpha-non-expansive multi-valued mappings from the Banach space setting to a convex metric space. Two examples of generalized alpha-non-expansive multi-valued mappings are presented, and it is numerically shown that our iteration scheme enables faster convergence than other well-known schemes in the literature. To demonstrate the application of one of our results, we provide the solution of a non-linear integral equation.

This paper introduces a novel inertial forward-backward-forward algorithm driven by a newly conceptualized moving point projection technique for solving monotone inclusion problems in real Hilbert spaces. By leveraging the properties of a Lipschitz continuous, monotone operator and a maximally monotone operator alongside this innovative projection strategy, we dynamically construct a sequence of nonempty, closed, and convex sets that contain the zeros of the sum of the two operators. This geometric construction ensures that the resulting sequence is well defined and guarantees its weak convergence to a solution. Furthermore, to validate the practical efficacy of the proposed theoretical framework, we evaluate our method on image restoration problems. Numerical experiments measuring the improvement in signal-to-noise ratio (ISNR) and the structural similarity index measure (SSIM) confirm that the proposed algorithm is highly efficient and significantly outperforms existing state-of-the-art methods.

In this article, a reflected-proximal method for solving equilibrium problems is proposed. Using this method, weak and strong convergence results together with the rate of convergence are obtained under certain assumptions. The method requires only one computation of the proximal per iteration thereby making it less computationally expensive. Furthermore, the case when the feasible set is the set of fixed points of enriched nonexpansive mappings is considered for the reflected-proximal and non-reflected proximals. Finally, substantial results for a variational inequality problem are obtained as consequences of the main results. The results not only contribute theoretically but also discuss the practical effectiveness of the methods, as evidenced by illustrative examples.

In this article, we introduce a novel averaged-type iterative scheme designed for solving convex minimization problems over the set of common fixed points of a pair of demicontractive mappings. Under suitable assumptions, we prove that the proposed algorithm converges strongly to the solution of the considered problem in a Hilbert space setting. We further demonstrate the applicability of our method to quadratic optimization problems with a bounded linear operator. In addition, we also report the numerical experiments that were performed in order to demonstrate the convergence behavior of the algorithm and to highlight its superiority over related existing methods.

Let X be a nonempty set and d: X x X -> R+ a mapping (i.e., a distance) and J: X -> X a contraction. In this paper we study the following problem: Under which conditions on (X, d) do we have that F-integral (){subset of X|(integral )(x) = x) = {*}? Similar problems for R-distances, K-distances, (R+)-distances, and for extending distances are investigated. Applications to contractions on generalized (dislocated, quasi-, partial, ultra-) metric spaces, are also given. In order to study these problems we introduce the notion of suitable distance space for contractions. The paper [Berinde V., P & abreve;curar M., Rus L.A. Some classes of distance spaces as generalized metric spaces: terminology, mappings, fixed points and applications in Theoretical Informatics, Creat. Math. Inform. 34 (2025), no. 2, 155-174] is an heuristic introduction to the present one. Our results open new perspectives in the fixed point theory and theoretical computer science and have important applicability in denotational semantics, as semantic operators in most programming language paradigms satisfy the requirements of fixed point principles for contractions on generalized metric spaces.

This paper presents an adaptive algorithm for solving enriched contraction variational inequality problems, using the set of fixed points of an enriched nonexpansive mapping as a constrained set. The algorithm is defined within the framework of unique geodesic spaces. In each iteration, the scheme uses only two embedded geodesic segments and does not require the computation of any metric projection. The method requires one evaluation of an enriched nonexpansive mapping T-1 and an enriched contraction T-2 at every iteration. The convergence analysis of the proposed scheme is performed in the setting of CAT(0) spaces, and a numerical example is provided to support the findings.

We consider new iterative algorithms for solving split common solution problems in the class of demicontractive mappings. These algorithms are obtained by inserting an averaged term into the algorithms previously used in [He, Z. and Du, W-S., Nonlinear algorithms approach to split common solution problems, Fixed Point Theory Appl. 2012, 2012:130, 14 pp] for the case of quasi-nonexpansive mappings. In this way, we are able to solve the split common solution problem in the larger class of demicontractive mappings, which strictly includes the class of quasi-nonexpansive mappings. Our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space.

In this paper, we establish some coincidence point theorems and common fixed point theorems for nonself G-almost contractions in Banach spaces endowed with a directed graph and display some examples to confirm our main results. Our main theorems extend and generalize many known theorems in this area.

In this paper, we consider iterated function systems built using a finite family of condensing enriched phi-contractions w.r.t. a measure of noncompactness in Banach spaces. We prove the existence of a fractal associated to the above mentioned iterated function system.

In this paper we present a point of view on the terminology of distance spaces (names, basic notions, convergence sequence, Cauchy sequence, contraction mapping, induced order, associated metric,...) and corresponding contraction principle, and fixed point principle of increasing mappings, in such spaces. Applica tions to theoretical computer science are also considered

This paper analyzes seven substantial distinct classes of contractive-type mappings using the technique of geodesic average perturbation within the framework of CAT(0) spaces. These classes of mappings are shown to be either saturated, in the sense that the geodesic average perturbation technique does not yield any significant new fixed point results, or unsaturated, in the sense that the technique provides genuine new fixed point results. The results establish that the class of strictly pseudocontractive self-mappings and the class of demicontractive self-mappings are saturated. Furthermore, the unsaturated category includes the class of Banach contractions, the class of Kannan contractions, the class of Bianchini contractions, the class of nonexpansive mappings, and the class of Ćirić–Reich–Rus contraction mappings. Our findings extend results from Hilbert spaces to convex (in the geodesic sense) metric spaces. This work provides an avenue for investigating fixed point results for several other important classes of contractive mappings using the geodesic average perturbation technique within the framework of geodesic spaces such as Hadamard manifolds, Hilbert balls, hyperbolic spaces, and CAT(k) spaces for some k ∈ℝ .

We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in the literature from the class of nonexpansive or quasi-nonexpansive mappings to the larger class of demicontractive mappings. Examples to illustrate numerically the effectiveness of the new analytical results are presented.

This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and establish the strong convergence of the sequences generated by this method to the common solution for the fixed point problem and the variational inequality problem. In order to illustrate the feasibility of the hypotheses and the superiority of our theoretical results over the existing literature, an example is also presented.

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 ex- plore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specif- ically, 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.

The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings established by the authors and their collaborators by using this technique; and third, to survey some related developments in the very recent literature which were authored by other researchers.

In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings J. Inequal. Appl. 131 (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results.

This paper presents the variational inequality problem in CAT(0) spaces, with the underlying operator being an enriched nonexpansive mapping. The existence of a solution to the problem is discussed with fixed points of the mapping. The paper presents substantial properties of the problem, including convergence analyses of certain bounded nets. The regularized version of the problem is also analyzed, leading to the proposal of an inexact proximal point scheme for approximating fixed points of the mapping that also solves the problem. Under different mild conditions, the sequences generated from the proposed algorithm are shown to Delta-converge to a fixed point which solves the problem.

We give a brief account on a basic result (Lemma \ref{lem2}) which is a very useful tool in proving various convergence theorems in the framework of the iterative approximation of fixed points of demicontractive mappings in Hilbert spaces. This Lemma relates the class of quasi-nonexpansive mappings, by one hand, and the class of $k$-demicontractive mappings (quasi $k$-strict pseudocontractions), on the other hand and essentially states that the class of demicontractive mappings, which strictly includes the class of quasi-nonexpansive mappings, can be embedded in the later by means of an averaged perturbation. From the point of view of the fixed point problem, this means that any convergence result for Krasnoselskij-Mann iterative algorithms in the class of $k$-demicontractive mappings can be derived from its corresponding counterpart from quasi-nonexpansive mappings.