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The aim of this paper is to generalize the results on expansive mappings of Yesilkaya and Aydin from Fixed Point Results of Expansive Mappings in Metric Spaces [see Yesilkaya, S. S.; Aydin, C. Fixed Point Results of Expansive Mappings in Metric Spaces. Mathematics 8 (2020), 1800]. In the present paper we show that the conditions imposed on the function 9 can be relaxed. Thus, we present more general fixed point results for q-expansive mappings in metric spaces and prove some fixed point theorems for this class of mappings, via a different approach. Finally, we present some examples to support the new results. [ABSTRACT FROM AUTHOR]

We are concerned in this paper with the convergence analysis of the primal-dual splitting (PDS) and the split Douglas-Rachford (SDR) algorithms for monotone inclusions by using an operator-oriented approach. We shall show that both PDS and SDR algorithms can be driven by a (firmly) nonexpansive mapping in a product Hilbert space. We are then able to apply the Krasnoselskii-Mann and Halpern fixed point algorithms to PDS and SDR to get weakly and strongly convergent algorithms for finding solutions of the primal and dual monotone inclusions. Moreover, an additional projection technique is used to derive strong convergence of a modified SDR algorithm. [ABSTRACT FROM AUTHOR]

The main aim of this paper is omitting some superfluous assumptions in the definition of the class of functions Θ, by means of which were defined and studied various classes of ϑ-contractions, and still obtaining the uniqueness of the fixed point for this new type of contractive mappings. Several generalizations of continuous ϑ-contractions are presented along with their applications to the study of integral equations. [ABSTRACT FROM AUTHOR]

This paper considers a model for population dynamics with age structure. Following Dufresne (2006) and Beghriche et all (2022) the probability of survival is assumed to be a linear combination of exponentials, and a product of a polynomial and an exponential. The number of births in unit time is characterized through a system of ordinary differential equations. This is solved explicitly in special cases, which leads to closed form expressions for the population size. The later allows an assymptotic analysis with three cases; the population goes extinct, explodes, or converges to a finite number depending of the interplay between model parameters. From a practical standpoint our modelling approach leads to a better fit of population data when compared to the exponential survival, and it also allows for more shapes of population as a function of time. [ABSTRACT FROM AUTHOR]

In this paper, we survey iterative algorithms for solving split variational inequalities and fixed point problems in Hilbert spaces. The investigated split problem is involved in two pseudomonotone operators and two pseudocontractive operators. We propose a self-adaptive Tseng-type algorithm for finding a solution of the split problem. Strong convergence of the suggested algorithm is shown under weaker conditions than sequential weak-to-weak continuity imposed on two pseudomonotone operators. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for solving variational inclusion problems in Hilbert spaces. This algorithm uses two inertial terms to speed up the convergence. In order to avoid computing the Lipschitz stepsize, we use an updated stepsize which is not necessary to know the Lipschitz constant of the operator. The weak convergence is established under some mild conditions. We present numerical performance of the proposed algorithm and compare our algorithm with other algorithms in literature. Finally, we deduce our algorithm for solving the convex minimization problem and give an application to the data classification problem of heart failure dataset. [ABSTRACT FROM AUTHOR]

The Collatz conjecture is an open problem involving the 3x +1 function. The function belongs to a class of generalized 3x + 1 functions of relatively prime type. This paper focuses on exploring periodic cycles for an extension of a generalized 3x + 1 function of relatively prime type. By extending its domain to R, the result shows that every integer periodic point is isolated in the usual topology on R. Moreover, every positive integer periodic cycle for the extension is attracting if the generalized 3x + 1 function is specified by parameters under some conditions. [ABSTRACT FROM AUTHOR]

We introduce a novel class of asymptotically α-hemicontractive mappings and demonstrate its relationship with the existing related families of mappings. We establish certain interesting properties of the fixed point set of the new class of mappings. Furthermore, we propose and investigate a new iterative algorithm for solving split common fixed point problem for the new class of mappings. In particular, weak and strong convergence theorems for solving split common fixed point problem for our new class of mappings in Hilbert spaces are proved. Moreover, using our method, we require no prior knowledge of norm of the transfer operator. The results presented in the paper extend and improve the results of Censor and Segal [Censor, Y.; Segal, A. The split common fixed point problem for directed operators. J. Convex Anal. 16 (2009), no. 2, 587-600.], Moudafi [Moudafi, A. The split common fixed-point problem for demicontractive mappings. Inverse Problems 26 (2010), no. 5:055007.; Moudafi, A. A note on the split common fixed-point problem for quasi-nonexpansive operators. Nonlinear Anal. 74 (2011), no. 12, 4083-4087.], Chima and Osilike [Chima, E. E.; Osilike, M. O. Split common fixed point problem for class of asymptotically hemicontractive mappings. J. Nigerian Math. Soc. 38 (2019), no. 3, 363-390.], Fan et al [Fan, Q.; Peng, J.; He, H. Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators. Optimization 70 (2021), no. 5-6, 1409-1423.] and host of other related results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of fractional equations with nonlinear boundary condition. We establish a new comparison principle related to linear fractional equation and show the existence of extreme solution by using monotone iterative method and lower and upper solutions method. [ABSTRACT FROM AUTHOR]

Starting from a characterization of polynomial dichotomy by means of admissibility, recently proved in [Dragicevic, D.; Sasu, A. L.; Sasu, B. Admissibility and polynomial dichotomy of discrete nonautonomous systems. Carpath. J. Math. 38 (2022), 737-762.], the aim of this paper is to explore the roughness of polynomial dichotomy in the presence of perturbations and to obtain a new robustness criterion. We show that the polynomial dichotomy is robust when subjected to linear additive perturbations which are bounded by a well-chosen sequence. We emphasize that the new bounds imposed to the perturbation family improve and extend the previous approaches. Furthermore, we mention that the main result applies to discrete nonautonomous systems in Banach spaces with the only requirement that their propagators exhibit a polynomial growth. [ABSTRACT FROM AUTHOR]

In this paper we introduce new effective technique for investigation of oscillation for second-order differential equation with mixed argument (E) y"(t) = p(t)y(τ (t)). Our criteria improves the existing ones and the progress is illustrated via several examples. [ABSTRACT FROM AUTHOR]

The paper investigates a new type of contraction called (M, K, ψ)-HR-Ćirić-Reich-Rus contractions, which extends the existing research on Ćirić-Reich-Rus contraction mappings. We prove fixed point theorems by enriching (M, K, ψ)-HR-Ćirić-Reich-Rus contractions with respect to the asymptotic regularity of generalized averaged mappings. These mappings are denoted as Tφ = (1 - φ) I + φT, where I is the identity map and φ is a function from a normed space to real numbers. [ABSTRACT FROM AUTHOR]

The paper considers impulsive systems with singularities. The main novelty is that beside the singularity of the differential equation, the impulsive equation is a singular one. The method of boundary functions is applied to obtain the main result. Examples with simulations confirming the theoretical results are given. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes a new viscosity approximation method with the inertial technique for finding a common fixed point of a countable family of nonexpansive mappings and then its strong convergence theorem is established under some suitable conditions. As a consequence, we employ our proposed algorithm for solving some convex bilevel optimization problems and then apply it for solving regression of a graph of cosine function and classification of some noncommunicable diseases by using the extreme learning machine model. We perform a comparative analysis with other algorithms to demonstrate the performance of our approach. Our numerical experiments confirm that our proposed algorithm outperforms other methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to modify proximal operators in Hilbert spaces. We introduce an intermixed algorithm with viscosity technique to find the solution of fixed point problem of two proximal operators in a real Hilbert space, utilizing the modified proximal operators. Under some mild conditions, a strong convergence theorem is established for the proposed algorithm. We also apply our main result to the split feasibility problem. Finally we provide numerical examples for supporting the main result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new inertial iterative algorithm involving the linesearch rule for the split variational inclusion in real Hilbert spaces. We use two inertial terms to accelerate the convergence speed of the proposed algorithm. Under suitable conditions, we prove its weak convergence theorem. Finally, in applications, we apply our algorithm to image deblurring and data classification problem in predicting diabetes mellitus. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and uniqueness of solutions for a system of Hilfer-Hadamard sequential fractional differential equations using standard fixed-point theorems. We apply the Leray-Schauder alternative and Banach's contraction mapping principle to obtain the existence and uniqueness results for the given problem. Additionally, we discuss illustrative examples. [ABSTRACT FROM AUTHOR]

The goal of this paper is to examine both necessary and sufficient conditions for a specific feasible point to be a global minimizer for reverse quasiconvex programming problems. These results are obtained in terms of adequate approximate subdifferentials and can be viewed as the problem of a convex maximization problem constrained by a convex set. Sufficient conditions for optimality are also established in terms of the Greenberg-Pierskalla subdifferential. Illustrative examples are also given to illustrate the significance of the obtained results. [ABSTRACT FROM AUTHOR]

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

This paper presents a two inertial technique with a projection Mann forward-backward splitting algorithm for solving variational inclusion problems that exhibit weak convergence under suitable conditions in Hilbert spaces. Furthermore, we provide a numerical example in infinitely dimensional spaces to support the main result. Finally, we provide an application for data classification using an extreme learning machine. According to data provided by theWorld Health Organization (WHO), stroke is recognized as the predominant contributor to mortality and disability on a global scale. To appraise the efficacy of our algorithm, we procured a dependable dataset for stroke prediction from the Kaggle website. The best algorithm that performed this task is ours compared to other machine learning methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified inertial extragradient algorithm with non-monotonic step sizes for approximating a common solution of the pseudomonotone equilibrium problem and the fixed point problem for the quasi-nonexpansive mapping in the framework of a real Hilbert space. Under some constraint qualifications of the scalar sequences, the strong convergence theorem of the introduced algorithm is presented by using the self-adaptive non-monotonic step size without prior information about the Lipschitz constants of bifunction. Some numerical experiments are provided to demonstrate the computational efficiency and advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the framework of CATp(0) spaces and analyzes coupled best proximity points for cyclic Kannan and cyclic Chatterjea contractions. The framework is substantial and versatile for employing metric notions and contractive conditions. For each mapping, we establish the existence and uniqueness of the coupled best proximity point. The work gives a step toward investigating the best proximity points in CATp(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of (F, G)-perturbed contraction in a metric space and we establish some fixed point theorems which extends the results from Branga, A. N. Olaru, I. M. Some Fixed Point Results in Spaces with Perturbed Metrics. Carpathian J. Math. 38 (2022), no. 3, 641–654 and Olaru, I. M.; Secelean, N. A. A new approach of some contractive mappings on metric spaces. Mathematics 9 (2021), 1433. Also, an application to an integral equation and some illustrative examples are given throughout the paper. [ABSTRACT FROM AUTHOR]

In this paper, we make a comprehensive comparison in terms of the quality of the achieved solutions, the corresponding execution time and impact of the genetic operators on the quality of the results between the Haploid Genetic Algorithms (HGAs) and Diploid Genetic Algorithms (DGAs). The standard genetic algorithms, referred to in our paper as HGAs are characterized by the fact that they are using a haploid representation relating an individual with a chromosome, while the DGAs are using diploid individuals which are made of two chromosomes corresponding to the dominant and recessive genes. Even though the general opinion is that DGAs do not provide much benefit as compared to classical GAs, based on extensive computational experiments, we do show that the DGAs are robust, have a high degree of consistency and perform better, sometimes almost twice as well, than the HGAs, but are slower due to the high number of operations to be performed, caused by the duplication of the genetic information. However, the quality of the solutions achieved by the DGAs compensate their relative high execution time. The better quality of the DGAs, proving the efficiency of using diploid genes, is given by the homogeneity of the population which covers the search space thoroughly and in this way being capable of avoiding the local optima. [ABSTRACT FROM AUTHOR]

Let Pn := H*((RP∞)n) =≈ Z2[x1, x2, ..., xn] be the graded polynomial algebra over K, where K denotes the prime field of two elements. We investigate the Peterson hit problem for the polynomial algebra Pn, viewed as a graded left module over the mod-2 Steenrod algebra, A. For n > 4, this problem is still unsolved, even in the case of n = 5 with the help of computers. In this paper, we study the hit problem for the case n = 6 in degree dk = 6(2k - 1) + 9.2k, with k an arbitrary non-negative integer. By considering K as a trivial A-module, then the hit problem is equivalent to the problem of finding a basis of K-graded vector space KAPn. The main goal of the current paper is to explicitly determine an admissible monomial basis of the K-graded vector space KAP6 in some degrees. At the same time, the behavior of the sixth Singer algebraic transfer in degree dk = 6(2k - 1) + 9.2k is also discussed at the end of this article. Here, the Singer algebraic transfer is a homomorphism from the homology of the mod-2 Steenrod algebra, Torn,n+dA(K,K), to the subspace of K A Pn consisting of all the GLn-invariant classes of degree d. [ABSTRACT FROM AUTHOR]

In this paper, by using symmetric first-order divided differences, we introduce a new family of Secant-like iterative methods with quadratic convergence. Afterthought, we analyze its semilocal and local behavior when the nonlinear operator F is not differentiable by imposing appropriate bounding conditions in each case. Theoretical results have also been tested by solving a problem which shows the applicability of our work. [ABSTRACT FROM AUTHOR]

The concept of demicontractive operators introduced by Ştefan Măruşter is widely used in application and has been investigated by many scholars. The purpose of this paper is to continue to survey iterative methods for solving the split problem relevant to demicontractive operators. With the help of fixed point techniques, we construct an iterative sequence for solving the split fixed point problem in which three demicontractive operators are involved. Strong convergence result is obtained under several additional conditions. Finally, two numerical examples are given to illustrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper we will study a Voronovskaja type theorem and a simultaneous approximation result for a new class of generalized Bernstein operators. The new operators are obtained using a generalization of Kantorovich's method, namely, we will introduce a sequence of operators Kln = Dl ... Bn+l ... Il, where Bn+l are Bernstein operators, Dlf = f(l) + al-1f(n-1) + · · · + a1f' + a0f is a differential operator with constant coefficients aj, j ∈ {0, . . ., l - 1} and Il a corresponding antiderivative operator such that Dl ... Il = Id. [ABSTRACT FROM AUTHOR]

In this paper, we modified proximal point algorithm with some convex combination technique to approximate a minimizer, equilibrium point and a common fixed point of a family of nonexpansive mappings in Hilbert spaces. We establish a weak convergence theorem under some mild conditions. Moreover, we also provide a numerical example to illustrate the convergence behavior of the proposed iterative method. [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]

This paper presents equilibrium problems and their regularized problems in the framework of Hadamard spaces. Using the concept of tangent space products, we introduce a resolvent operator and deduce essential properties in relation to equilibrium problem. Furthermore, we analyze the regularized problems involving resolvent operators. Finally, we establish two convergence results concerning proximal algorithms. [ABSTRACT FROM AUTHOR]

In this article, we consider and investigate a split convex feasibility problem involving two bounded linear operators in Hilbert spaces. We introduce a self-adaptive CQ-type algorithm by selecting the stepsize which is independent of the operator norms and establish a strong convergence result of the proposed algorithm under some mild control conditions. Moreover, we propose a self-adaptive relaxed CQ-type algorithm for solving the problem constrained by sub-level sets of convex functions. A numerical example and an application in compressed sensing are also given to illustrate the convergence behaviour of our proposed algorithms. Our results in this paper improve and generalize some existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, new effective technique for investigation of the higher order differential equation (E) y(n)(t) = p(t)y(τ(t)). is established. We offer new criteria for excluding certain types of nonoscillatory solutions which improve all existing results from the literature. Examples are provided to illustrate the importance of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we study several classes of split inverse problems. We start with the split common fixed point problem with multiple output sets for multivalued demicontractive mappings. A relaxed inertial iterative method for solving this problem is presented and analysed. Furthermore, the method is applied to a system of split variational inequalities, system of split equilibrium problem and other related split problems. Several numerical experiments illustrate and validate the applicability of our proposed method. [ABSTRACT FROM AUTHOR]

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of this paper is to give the crossing numbers of the join products of seven graphs on six vertices with paths and cycles on n vertices. The proofs are done with the help of several well-known auxiliary statements, the idea of which is extended by a suitable classification of subgraphs that do not cross the edges of the examined graphs. Finally, for m at least three and n = 5, we also establish the validity of a conjecture introduced by Stas and Valiska concerning the crossings numbers of the join products of ˇ the wheels on m + 1 vertices with the paths on n vertices. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two inertial self-adaptive projection and contraction methods for solving the pseudomonotone variational inequality problem with a Lipschitz-continuous mapping in real Hilbert spaces. The adaptive stepsizes provided by the algorithms are simple to update and their computations are more efficient and flexible. Also we prove some weak and strong convergence theorems without prior knowledge of the Lipschitz constant of the mapping. Finally, we present some numerical experiments to demonstrate the effectiveness of the proposed algorithms by comparisons with related methods and some applications of the proposed algorithms to the image deblurring problem. [ABSTRACT FROM AUTHOR]

Starting from an initial triangle, one may wish to check whether a sequence of iterations is convergent, or is convergent in some shape, and to find the limit. In this paper we first prove a general result for the convergence of a sequence of nested triangles (Theorem 2.2), then we study some properties of the power curve Γ of a triangle. These are used to prove that the sequence of nested triangles defined by a point Q(s) on the power curve converges to a point for every s ∈ [0, 2] (Theorem 4.2). In particular, we obtain that the sequence of nested triangles defined by the incenter converges to a point, completing the main result in [14]. Finally, we present some numerical simulations which inspire open questions regarding the convergence of such iterations. [ABSTRACT FROM AUTHOR]

The paper considers a stochastic differential equation of Duffing type with Markov coefficients. The existence of unpredictable solutions is considered. The unpredictability is a property of bounded functions characterized by unbounded sequences of moments of divergence and convergence in Bebutov dynamics. Markov components of the equation coefficients admit the unpredictability property. The components of the equation coefficients are derived from a Markov chain. The existence, uniqueness and exponential stability of an unpredictable solution are proved. The sequences of divergence and convergence of the coefficients and the solution are synchronized. Numerical examples that support the theoretical results are provided. [ABSTRACT FROM AUTHOR]

In a recent paper (I. A. Rus. Sets with structure, mappings and fixed point property: fixed point structures. Fixed Point Theory 23 (2022), No. 2) the author introduced, amongst others, the following notions: set-mapping pair and set-mapping pair bijection. In this paper we study the set-mapping pair bijections in connection with the isomorphisms structure, and their impact on the fixed point theory in a set-mapping pair. Some open problems are also formulated. [ABSTRACT FROM AUTHOR]

In this paper, the concept of perturbed metric was introduced within the metric spaces and some fixed point results were established for self-mappings satisfying such contractive conditions, using Picard operators technique and generalized contractions. Moreover, some applications of the main result to continuous data dependence of the fixed points of Picard operators defined on these spaces were presented. Also, the main result of this paper was applied to study the existence and uniqueness of the solution for an integral equation which models an epidemiological problem. [ABSTRACT FROM AUTHOR]

This paper introduces a new improved method for obtaining the oscillation of a second-order advanced difference equation of the form is a monotonically increasing integer sequence. We derive new oscillation criteria by transforming the studied equation into the canonical form. The obtained results are original and improve on the existing criteria. Examples illustrating the main results are presented at the end of the paper. [ABSTRACT FROM AUTHOR]

In the present paper we study the relationships between different concepts of convex structures in metric spaces that that are related to the works of K. Menger [Menger, K. Untersuchungen über allgemeine Metrik. Math. Ann. 100 (1928), 75-163], H. Busemann [Busemann, H. The geometry of geodesics, Academic Press, 1955], I. N. Herstein; J. Milnor [Herstein, I. N.; Milnor, J. An axiomatic approach to measurable utility. Econometrica 21 (1953), 291-297], E. Michael [Michael, E. Convex structures and continuous selections. Canad. J. Math. 11 (1959), 556-575], A. Nijenhuis [Nijenhuis, A. A note on hyperconvexity in Riemannian manifolds. Canad. J. Math. 11 (1959), 576-582.], W. Takahashi; T. Shimizu [Shimizu, T.; Takahashi, W. Fixed points of multivalued mappings in certain metric spaces. Topol. Methods Nonlinear Anal. 8 (1996), no. 1, 197-203 and Takahashi, W. A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22 (1970), 142-149], M. Taskovi'c [Taskovi'c, M. General convex topological spaces and fixed points. Math. Moravica 1 (1997), 127-134], Yu. A. Aminov [Aminov, Yu. A. Two-Dimensional Surfaces in 3-Dimensional and 4-Dimensional Euclidean Spaces. Results and Unsolved Problems. Ukr. Math. J. 71 (2019), no. 1, 1-38.], H. V. Machado [Machado, H. V. A characterization of convex subsets of normed spaces. Kodai Math. Sem. Rep. 25 (1973), 307-320], and many other papers. Some well known examples of concrete convex structures are reexamined and the possibilities of different embeddings of metric spaces with convex structures are also studied. Corollary 6.1 states that the Bolyai-Lobachevskii plane and the Bolyai-Lobachevskii half-plane are not isometrically embedding in some strictly convex normed space. A characteristic of the invariant metric generated by a norm is presented (Proposition 4.6). [ABSTRACT FROM AUTHOR]

This paper addresses the issue of which strong duality holds between parametric robust semi-definite linear optimization problems and their dual programs. In the case of a spectral norm uncertainty set, it yields a corresponding strong duality result with a semi-definite programming as its dual. We also show that the dual can be reformulated as a second-order cone programming problem or a linear programming problem when the constraint uncertainty sets of parametric robust semi-definite linear programs are given in terms of affinely parameterized diagonal matrix. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the intermixed algorithm in p-uniformly convex metric spaces, and then we prove Δ-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete p-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove Δ-convergence to solve the minimization problems in the framework of complete p-uniformly convex metric spaces. Finally, we give two examples in Lp spaces and numerical examples to support our main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider an iterative approximation problem of split variational inequalities in Hilbert spaces. In order to solve this split problem, we construct an iterative algorithm which combines a forward-backward-forward method and a self-adaptive rule to update the step-sizes. We prove that the constructed algorithm converges strongly to a solution of the split variational inequalities under some mild assumptions. [ABSTRACT FROM AUTHOR]

In mathematical psychology, themodel of decision practice represents the development ofmoral judgment that deals with the time to decide themeaning of the various choices and selecting one of themfor use. Most animal behavior research classifies such situations as two distinct phenomena. On the other hand, reward plays a big part in this kind of study since, based on the selected side and food location, such circumstances may be classified into four categories. This paper intends to investigate such types of behavior and establish a general functional equation for it. The proposed functional equation can be used to describe several psychological and learning theory models in the existing literature. By using the fixed point theory tools, we obtain the results related to the existence, uniqueness, and stability of a solution to the proposed functional equation. Finally, we give two examples to support our main results. [ABSTRACT FROM AUTHOR]

The aimof this paper is to introduce two notions of Levitin--Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problemto be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painlevé--Kuratowski convergence of sequences of approximate solution sets are also established. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of which strong duality holds between parametric robust semi-definite linear optimization problems and their dual programs. In the case of a spectral norm uncertainty set, it yields a corresponding strong duality result with a semi-definite programming as its dual. We also show that the dual can be reformulated as a second-order cone programming problem or a linear programming problem when the constraint uncertainty sets of parametric robust semi-definite linear programs are given in terms of affinely parameterized diagonal matrix. [ABSTRACT FROM AUTHOR]

In this paper we present a mathematical model for studying the interactions between human immune systemand a pathogenic virus, such as Covid-19. Amathematical analysis based on dynamical systems theory is performed. More exactly, we model the interactions between the immune system and the virus by a modified predator-prey method. Several conclusions emerge from this study, and the main two of them are the followings: 1) a deficiency in the concentration of a single type of white blood cells in the early stages of virus proliferation may lead to the virus victory, and 2) if the number of at least one type of white blood cells can be increased beyond the normal threshold by medical interventions in the early stages of virus infection, then the immune system has a better chance to win against the virus. [ABSTRACT FROM AUTHOR]