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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

A very impressive research work has been devoted in the last two decades to obtaining fixed point theorems in quasimetric spaces (also called b-metric spaces). Some incorrect and incomplete references with respect to the early developments on fixed point theory in b-metric spaces are though perpetually taking over from the existing publications to the new ones. Starting from this fact, our main aim in this note is threefold: (1) to briefly survey the early developments in the fixed point theory on quasimetric spaces (b-metric spaces); (2) to collect some relevant bibliography related to this topic; (3) to discuss some other aspects of current interest in the fixed point theory on quasimetric spaces (b-metric spaces). [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 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 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, 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 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]

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]

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, 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]

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. In the paper, the crossing number of the join product G* + Dn for the connected graph G* on six vertices consisting of one path on four vertices P4 and two leaves adjacent with the same outer vertex of the path P4 is given, where Dn consists of n isolated vertices. Finally, by adding some edges to the graph G*, we obtain the crossing numbers of the join products of other four graphs with Dn. [ABSTRACT FROM AUTHOR]

We study in this paper conditions under which nilradicals of totally disconnected locally compact rings are closed. In the paper is given a characterization of locally finite compact rings via identities. [ABSTRACT FROM AUTHOR]

In this paper, we look at Diophantine triples with values in three different binary recurrence sequences. These are the Fibonacci and Pell sequences and the sequence of one more of powers of a given prime p. The novelty of the article is the appearance of three different sequences, as up to now the analogous problem had been investigated only for one sequence. [ABSTRACT FROM AUTHOR]

In the paper, we consider the simultaneous approximation of a collection of analytic functions by a collection of shifts of the Riemann zeta-function (ζ(s + itα1τ ), . . ., ζ(s + itαrτ )), where tτ is the Gram function and α1, . . ., αr are different positive numbers. It is obtained that the set of such shifts has a positive lower density. [ABSTRACT FROM AUTHOR]

In this paper we provide some properties and applications of MV-algebras. We prove that a Fibonacci stationary sequence in an MV-algebra gives us an idempotent element. Moreover, taking into account of the representation of a finite MV-algebra, by using Boolean elements of this algebra, we prove that a Fibonacci sequence in an MV-algebra is always stationary. This result is interesting comparing with the behavior of such a sequence on the group (Zn, +), where the Fibonacci sequences are periodic, with the period given by the Pisano period. We also give some examples of finite MV-algebras and the number of their idempotent elements. As an application in Coding Theory, to a Boolean algebra it is attached a binary block code and it is proved that, under some conditions, the converse is also true. [ABSTRACT FROM AUTHOR]

In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature. [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]

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 paper considers three concepts of uniform instability for evolution operators: uniform exponential instability, uniform polynomial instability and uniform h-instability. Some characterizations of these notions and connections between these concepts are given. [ABSTRACT FROM AUTHOR]

In this paper we prove that an interesting result concerning the generalized Hyers-Ulam stability of the linear functional equation g(ϕ(x)) = a(x) • g(x) on a complete metric group, given in 2014 by S.M. Jung, D. Popa and M.T. Rassias, can be obtained using the fixed point technique. Moreover, we give a characterization of the functions that can be approximated with a given error, by the solution of the linear equation mention above. Our results are also related to a recent result of G.H. Kim and Th.M. Rassias concerning the stability of Psi functional equation. [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 deals with the analysis of a discrete-time Cournot game with time delay, where the interactions of one public firm and n private firms on the market are considered. The production of the public firm is adjusted based on the past production levels of the private firms. At the same time, the productions of the private firms are updated with respect to the past production of the public firm. Two equilibrium points are determined for the discrete-time nonlinear mathematical model. The analysis of the stability reveals that the boundary equilibrium point is a saddle point, while the positive one, under some conditions, is asymptotically stable for any time delays. Numerical simulations illustrate the complex dynamic behaviour of the system. [ABSTRACT FROM AUTHOR]

In this paper we provide a new approach in the study of a variational-hemivariational inequality in Hilbert space, based on the theory of maximal monotone operators and the Banach fixed point theorem. First, we introduce the inequality problem we are interested in, list the assumptions on the data and show that it is governed by a multivalued maximal monotone operator. Then, we prove that solving the variational-hemivariational inequality is equivalent to finding a fixed point for the resolvent of this operator. Based on this equivalence result, we use the Banach contraction principle to prove the unique solvability of the problem. Moreover, we construct the corresponding Picard, Krasnoselski and Mann iterations and deduce their convergence to the unique solution of the variational-hemivariational inequality. [ABSTRACT FROM AUTHOR]

In the paper Operators on infinite dimensional cartesian product, (Analele Univ. Vest TimiŞoara, Mat. Inform., 48 (2010), 253-263), by I. A. Rus and M. A. Şerban, the authors give a generalization of the Fibre contraction theorem on infinite dimensional cartesian product. In this paper we give an application of this abstract result to an infinite system of differential equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some sequences of Euler type. We will explore the sequences (Fn)n=1, defined by Fn (x) = Pn k=1 f (k) - R n+x 1 f (t) dt, for any n = 1 and x [0, 1], where f is a local integrable and positive function defined on [1,8). Starting from some particular example we will find that this sequence is uniformly convergent to a constant function. Also, we present a stability result. [ABSTRACT FROM AUTHOR]

Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images. [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]

In this paper we shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Caratho'eodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of Dhage (2014) in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, a first-order iterative functional differential equation is investigated. With the help of the Schauder's fixed point theorem, we established some sufficient criteria that ensure the existence of positive periodic solutions. In addition, an application to three hematopoiesis models is also provided to corroborate the effeteness of our main findings. These last ones substantially enrich and complement some earlier works. [ABSTRACT FROM AUTHOR]

In the paper, we study the oscillation of the half-linear second-order differential equations with deviating argument of the form We introduce new monotonic properties of nonoscillatory solutions and use them to offer new criteria for elimination of certain types of solutions. The presented results essentially improve existing ones even for linear differential equations. [ABSTRACT FROM AUTHOR]

In this paper we consider a general integral operator for analytic functions in the open unit disk U and we obtain sufficient conditions for univalence of this integral operator, using Mocanu's and S,erb's Lemma. This integral operator was considered in a recent work Barbatu, C. and Breaz, D., [ The univalence conditions for a general integral operator, Acta Univ. Apulensis Math. Inform., 51 (2019), 75-87]. The results derived in this paper are shown to follow upon specializing the parameters involved in our results. Several corollaries of the main results are also considered. [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]

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]