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We propose a spatial equilibrium problem for a pulp and paper supply chain network under the Emission Trading System (ETS) and the circular economy principles. The developed closed-loop supply chain model, based on the variational inequality theory, accounts for the forest deployment and the production of paper using both virgin pulp and recyclable paper waste in an area that is subject to the ETS. In addition, it considers the exchanges of virgin pulp, paper, recyclable and not-recyclable paper waste between this regulated area and geographical zones where no environmental policies apply. The aim of this paper is to investigate the ETS impacts on the pulp and paper industries located in an environmentally regulated area in terms of operating costs, production and trading volumes of the aforementioned commodities, and emissions generated. The case study focuses on the European pulp and paper companies, which are among the energy-intensive industries deemed to be exposed to the carbon leakage risk as a consequence of the ETS application. Sensitivity analyses on the carbon price value and on the trade flexibility are conducted. Our results show that the ETS implies additional costs for the European pulp and paper companies and induces them to resort more on imports of virgin pulp and paper from not-regulated zones. [ABSTRACT FROM AUTHOR]

By using the uniformly ellipticity of linear partial differential operators (which contain p-Laplacian operators with $ 1 \lt p \lt \infty $ 1 < p < ∞), weak comparison principle and Urysohn's lemma, in the paper, we introduce and study a class of new variational inequalities involving uniformly elliptic operators and demicontinuous S-contractive operators to extend some corresponding tasks and scope on population genetics. Further, as applications, we employ the main results presented in this paper to second-order uniformly elliptic inequalities and a population model of one species arising in disrupted environments. [ABSTRACT FROM AUTHOR]

In this paper, we present an inertial projection and contraction algorithm (IPCA for short) for variational inequality problems (VIP for short) without Lipschitz continuity of the underlying mapping in Euclidean space. To obtain a larger step, the next iterate point of IPCA is generated by projecting the current iterate point onto a selected half-space, which is selected from finite half-spaces (one half-space can strictly separate the current iterate point from the solution set of VIP and other half-spaces are all contain the solution set of VIP) and has the largest distance to the current iterate point. Moreover, a new initial step-size strategy is used to accelerate IPCA. The global convergence of the sequence generated by IPCA is established. Numerical experiments show that IPCA can accelerate PCA both from the number of iterations point of view and the number of projections point of view. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The unique solvability of the considered second-order evolutionary inequality problem is established via a surjectivity result combined with a fixed point theorem. Moreover, we construct a regularized problem for such second-order evolutionary history-dependent variational–hemivariational inequality and show the convergence of the regularized solutions toward the solution of the original problem under some mild assumptions. [ABSTRACT FROM AUTHOR]

In this paper, for d ≥ 1 and s ∈ (0 , d 2) , we study the Bianchi–Egnell quotient Q (f) = inf f ∈ H ˙ s (R d) \ B ‖ (- Δ) s / 2 f ‖ L 2 (R d) 2 - S d , s ‖ f ‖ L 2 d d - 2 s (R d) 2 dist H ˙ s (R d) (f , B) 2 , f ∈ H ˙ s (R d) \ B , where S d , s is the best Sobolev constant and B is the manifold of Sobolev optimizers. By a fine asymptotic analysis, we prove that when d = 1 , there is a neighborhood of B on which the quotient Q (f) is larger than the lowest value attainable by sequences converging to B . This behavior is surprising because it is contrary to the situation in dimension d ≥ 2 described recently in König (Bull Lond Math Soc 55(4):2070–2075, 2023). This leads us to conjecture that for d = 1 , Q (f) has no minimizer on H ˙ s (R d) \ B , which again would be contrary to the situation in d ≥ 2 . As a complement of the above, we study a family of test functions which interpolates between one and two Talenti bubbles, for every d ≥ 1 . For d ≥ 2 , this family yields an alternative proof of the main result of König (Bull Lond Math Soc 55(4):2070–2075, 2023). For d = 1 we make some numerical observations which support the conjecture stated above. [ABSTRACT FROM AUTHOR]

In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate a class of nonconvex-constrained differential hemivariational inequalities consisting of nonlinear evolution equations and evolutionary hemivariational inequalities. The admissible set of constraints is closed and star-shaped with respect to a certain ball in a reflexive Banach space. We construct an auxiliary inclusion problem and obtain the existence results by applying a surjectivity theorem for multivalued pseudomonotone operators and the properties of Clarke subgradient operator. Moreover, the existence of a solution to the original problem is established by hemivariational inequality approach and a penalization method in which a small parameter does not have to tend to zero. Finally, an application of the main results is provided. [ABSTRACT FROM AUTHOR]

In this note, we give affirmative answers to two open problems posed by Agarwal et al. in the paper (J Optim Theory Appl 163(2):482-490, ). [ABSTRACT FROM AUTHOR]

This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a (P , η) -accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(.,.)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem. [ABSTRACT FROM AUTHOR]

Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. Let PC: X → C denote the (standard) metric projection operator. In this paper, we define the G a ^ teaux directional differentiability of PC. We investigate some properties of the G a ^ teaux directional differentiability of PC. In particular, if C is a closed ball or a closed and convex cone (including proper closed subspaces), then, we give the exact representations of the directional derivatives of PC. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the discussion of a new dynamical system involving a history-dependent variational-hemivariational inequality coupled with a non-linear evolution equation. The existence and uniqueness of the solution to this problem are established using the Rothe method and a surjectivity result for a pseudo-monotone perturbation of a maximal operator. Additionally, we derive the regularity solution for such a history-dependent variational-hemivariational inequality. Furthermore, the main results obtained in this study are applied to investigate the unique solvability of a dynamical viscoelastic frictional contact problem with long memory and wear. [ABSTRACT FROM AUTHOR]

First-order sufficient optimality conditions in terms of Lagrangian functions and Lagrange multipliers for nondifferentiable minimax programs and vector optimization problems in an Asplund space setting are obtained in this paper. Two illustrative examples are given. Our results implement the first-order necessary optimality conditions of Chuong and Kim (Ann Oper Res 251:73–87, 2017). [ABSTRACT FROM AUTHOR]

This paper is dedicated to the discussion of a new dynamical system involving a history-dependent variational-hemivariational inequality coupled with a non-linear evolution equation. The existence and uniqueness of the solution to this problem are established using the Rothe method and a surjectivity result for a pseudo-monotone perturbation of a maximal operator. Additionally, we derive the regularity solution for such a history-dependent variational-hemivariational inequality. Furthermore, the main results obtained in this study are applied to investigate the unique solvability of a dynamical viscoelastic frictional contact problem with long memory and wear. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. We propose an iterative algorithm which combines the hybrid steepest descent method with the inertial technique to solve this variational inequality problem. Strong convergence theorem of the proposed method is established under standard and mild conditions. Moreover, we do not require any prior information regarding the Lipschitz and strongly monotone constants of the mapping. The results of this paper improve and extend several known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish a minimal criterion of efficiency for a class of multiobjective variational control problems. Thus, some minimal conditions are formulated so that all local efficient solutions are also global. Also, we present an example to illustrate the mathematical developments derived in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalized multiple-set split feasibility problem including the common fixed-point problem for a finite family of generalized demimetric mappings and the monotone inclusion problem in 2-uniformly convex and uniformly smooth Banach spaces. We propose an inertial Halpern-type iterative algorithm for obtaining a solution of the problem and derive a strong convergence theorem for the algorithm. Then, we apply our convergence results to the convex minimization problem, the variational inequality problem, the multiple-set split feasibility problem and the split common null-point problem in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, by combining the inertial technique and the gradient descent method with Polyak's stepsizes, we propose a novel inertial self-adaptive gradient algorithm to solve the split feasibility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions. We examine the performance of our method on the sparse recovery problem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further. [ABSTRACT FROM AUTHOR]

Variational inequalities provide a framework through which many optimisation problems can be solved, in particular, saddle-point problems. In this paper, we study modifications to the so-called Golden RAtio ALgorithm (GRAAL) for variational inequalities—a method which uses a fully explicit adaptive step-size and provides convergence results under local Lipschitz assumptions without requiring backtracking. We present and analyse two Bregman modifications to GRAAL: the first uses a fixed step size and converges under global Lipschitz assumptions, and the second uses an adaptive step-size rule. Numerical performance of the former method is demonstrated on a bimatrix game arising in network communication, and of the latter on two problems, namely, power allocation in Gaussian communication channels and N-person Cournot completion games. In all of these applications, an appropriately chosen Bregman distance simplifies the projection steps computed as part of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, quasi-statical boundary contact problems of couple-stress viscoelasticity for inhomogeneous anisotropic bodies with regard to friction are investigated. We prove the uniqueness theorem of weak solutions using the corresponding Green's formulas and positive definiteness of the potential energy. To analyze the existence of solutions, we equivalently reduce the problem under consideration to a spatial variational inequality. We consider a special parameter-dependent regularization of this variational inequality which is equivalent to the relevant regularized variational equation depending on a real parameter, and study its solvability by the Galerkin approximate method. Some a priori estimates for solutions of the regularized variational equation are established and with the help of an appropriate limiting procedure, the existence theorem for the original contact problem with friction is proved. [ABSTRACT FROM AUTHOR]

In this paper, we study a new kind of generalized Caputo fractional differential quasi-variational inequalities in Hilbert spaces. We prove the uniqueness and the stability of the abstract inequality by using generalized singular Gronwall's lemma, projection operators, and contraction principle. Finally, an example is given to illustrate the abstract results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate mixed vector equilibrium-like problems (MVEPs) on Hadamard manifolds. Specifically, our aim is to establish error bounds for MVEPs. For this, we propose some regularized gap functions for MVEPs under suitable conditions. Then some error bounds for MVEPs in terms of regularized gap functions are obtained with the hypotheses imposed on the data of MVEPs. Our results in this paper are new and can be considered as a significant generalization of some previously known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a general oligopolistic market equilibrium model in which each firm produces several commodities in a time interval. To this aim, we introduce tensor variational inequalities in Hilbert spaces which are a powerful tool to analyse the model. Indeed we characterize the equilibrium condition by means of a suitable time-dependent tensor variational inequality. In addition, we prove some existence and regularity results and a numerical scheme to compute the solution. Finally we provide a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new relaxed inertial Tseng extragradient method with self-adaptive step size for approximating common solutions of monotone variational inequality and fixed point problems of quasi-pseudo-contraction mappings in real Hilbert spaces. We prove a strong convergence result for the proposed algorithm without the knowledge of the Lipschitz constant of the cost operator. Moreover, we apply our results to approximate solution of convex minimization problem, and we present some numerical experiments to show the efficiency and applicability of our method in comparison with some existing methods in the literature. Our proposed method is easy to implement. It requires only one projection onto a constructible half-space. [ABSTRACT FROM AUTHOR]

To address the split best proximity point and monotone variational inclusion problems in real Hilbert spaces, we present and investigate projection and viscosity approximation methods. Under a few reasonable assumptions, we prove some weak and strong convergence theorems for the aforementioned methods. The efficiency of the proposed method is demonstrated by some numerical examples. Some well-known recent results in this area have been improved, generalized, and extended as an outcome of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present an inertial Popov extragradient projection algorithm for solving multi-valued variational inequality problems in finite-dimensional Euclidean space. The global convergence of this algorithm is proved whenever the underlying mapping is Lipschitz continuous and pseudomonotone on the feasible set. Numerical experiments show that new algorithm is more efficient than algorithm of Ye [An improved projection method for solving generalized variational inequality problems. Optimization. 2018;67:1–11] whenever the underlying mapping is Lipschitz continuous. Here inertial technique can accelerate extragradient algorithm although the underlying mapping is multi-valued. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some new results on the Levitin–Polyak well-posedness to a class of split hemivariational inequality problems on Hadamard manifolds. We first consider a new class of split hemivariational inequality problems (for short, SHIP) on Hadamard manifolds and introduce the regularized gap functions for these problems. Then, we study the notion of Levitin–Polyak well-posedness by perturbations to SHIP and show the equivalence between the Levitin–Polyak well-posedness by perturbations and the existence of solutions for SHIP under suitable conditions. Furthermore, based on the regularized gap functions for the perturbed SHIP, we establish the criterion for the Levitin–Polyak well-posedness by perturbations for SHIP via the split optimization problems on Hadamard manifolds. Our main results presented in paper are new even in the special case of hemivariational inequality problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. Our first objective is to establish a new equivalence relationship between the graph convergence of a sequence of A ^ -maximal m-relaxed η -accretive mappings and their associated resolvent operators, respectively, to a given A ^ -maximal m-relaxed η -accretive mapping and its associated resolvent operator. We construct an iterative scheme for approximating a common element of the set of solutions of a system of generalized variational-like inclusions and the set of fixed points of a generalized nearly asymptotically nonexpansive mapping in the setting of real Banach spaces. As an application, the obtained equivalence conclusion is employed and under some appropriate conditions, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the above-mentioned two sets is verified. The second objective of this paper is to investigate and analyze the concept of H(.,.)-mixed mapping and the relevant results appeared in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. Our first objective is to establish a new equivalence relationship between the graph convergence of a sequence of A ^ -maximal m-relaxed η -accretive mappings and their associated resolvent operators, respectively, to a given A ^ -maximal m-relaxed η -accretive mapping and its associated resolvent operator. We construct an iterative scheme for approximating a common element of the set of solutions of a system of generalized variational-like inclusions and the set of fixed points of a generalized nearly asymptotically nonexpansive mapping in the setting of real Banach spaces. As an application, the obtained equivalence conclusion is employed and under some appropriate conditions, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the above-mentioned two sets is verified. The second objective of this paper is to investigate and analyze the concept of H(.,.)-mixed mapping and the relevant results appeared in the literature. [ABSTRACT FROM AUTHOR]

In the paper, we analyze problems of elasticity tensor identification for an elastic body with incorporated thin elastic and rigid inclusions in a non-coercive case. The inclusions are assumed to be delaminated from the surrounding elastic body, thus forming interfacial cracks. We consider inequality-type boundary conditions at the crack faces with unknown set of a contact to provide a mutual non-penetration between the crack faces. The considered problems are characterized by unknown displacement field and elasticity tensor. A formulation of identification problems includes an additional information, which can be found from a measurement. A solution existence of these problems is proved. [ABSTRACT FROM AUTHOR]

This paper proposes a new self-adaptive algorithm for solving the multiple-set split variational inequality problem in Hilbert spaces. Our algorithm uses dynamic step-sizes, chosen based on information of the previous step. In comparison with the work by Censor et al. [Numer Algorithms. 2012;59:301–323], the new algorithm gives strong convergence results and does not require information about the transformation operator's norm. Some applications of our main results regarding the solution of the multiple-set split feasibility problem and the split feasibility problem are presented and show that the iterative method converges strongly under weaker assumptions than the ones used recently by Xu [Inverse Probl. 2006;22:2021–2034] and by Buong [Numer Algorithms. 2017;76:783–798]. Numerical experiments on finite-dimensional and infinite-dimensional spaces and an application to discrete optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results. [ABSTRACT FROM AUTHOR]

Some properties of solutions of convex sweeping processes with velocity constraints are studied in this paper. Namely, the solution stability with respect to the initial value, the boundedness, the closedness, and the convexity of the solution set are discussed in detail. In addition, an outer estimate for the solution set is given here for the first time and two open questions are raised for further research. Our investigations complement the preceding ones on the solution existence and the solution uniqueness of convex sweeping processes with velocity constraints. [ABSTRACT FROM AUTHOR]

We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way in time (a Volterra absolutely continuous time-dependent sweeping process). The aim of our paper is twofold. The first one is to show the solvability of the initial value problem by setting up an appropriate catching-up algorithm (full discretization). This part is a continuation of our paper (Bouach et al. in arXiv: 2102.11987. 2021) where we used a semi-discretization method. Obviously, strong solutions and convergence of full discretization scheme are desirable properties, especially for numerical simulations. Applications to non-regular electrical circuits are provided. The second aim is to establish the existence of optimal solution to an optimal control problem involving the Volterra integro-differential sweeping process. [ABSTRACT FROM AUTHOR]

In this paper, a global efficiency criterion is established for a class of multidimensional variational control problems governed by first order PDE&PDI constraints and path-independent curvilinear integral cost functionals. More precisely, a minimal efficiency criterion for a local efficient solution to be its global efficient solution in the considered optimization problem is formulated and proved. Also, the theoretical developments derived in the paper are accompanied by an example of a nonconvex optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, an alternative approach is provided in the well-posedness analysis of elliptic variational–hemivariational inequalities in real Hilbert spaces. This includes the unique solvability and continuous dependence of the solution on the data. In most of the existing literature on elliptic variational–hemivariational inequalities, well-posedness results are obtained by using arguments of surjectivity for pseudomonotone multivalued operators, combined with additional compactness and pseudomonotonicity properties. In contrast, following (Han in Nonlinear Anal B Real World Appl 54:103114, 2020; Han in Numer Funct Anal Optim 42:371–395, 2021), the approach adopted in this paper is based on the fixed point structure of the problems, combined with minimization principles for elliptic variational–hemivariational inequalities. Consequently, only elementary results of functional analysis are needed in the approach, which makes the theory of elliptic variational–hemivariational inequalities more accessible to applied mathematicians and engineers. The theoretical results are illustrated on a representative example from contact mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we propose two inertial accelerated algorithms which do not require prior knowledge of operator norm for solving split feasibility problem with multiple output sets in real Hilbert spaces. We prove weak and strong convergence results for approximating the solution of the considered problem under certain mild conditions. We also give some numerical examples to demonstrate the performance and efficiency of our proposed algorithms over some existing related algorithms in the literature. [ABSTRACT FROM AUTHOR]

This paper deals with quasidifferentiable vector optimization problems involving invex functions wrt convex compact sets. We present vector variational-like inequalities of Minty type and of Stampacchia type in terms of quasidifferentials denoted by (QMVVLI) and (QSVVLI), respectively. By utilizing these variational inequalities, we infer vital and adequate optimality conditions for an efficient solution of the quasidifferentiable vector optimization problem involving invex functions wrt convex compact sets. We also establish various results for the solutions of the corresponding weak versions of the vector variational-like inequalities in terms of quasidifferentials. [ABSTRACT FROM AUTHOR]

In this paper we deal with a class of nonlinear quasi-variational inequalities involving a set-valued map and a constraint set. First, we prove that the set of weak solutions of the inequality is nonempty, weakly compact and upper semicontinuous with respect to perturbations in the data. Then, the results are applied to a quasi variational-hemivariational inequality of elliptic kind. Finally, as an illustrative applications we examine a mathematical model of a nonsmooth static frictional unilateral contact problem for ideally locking materials in nonlinear elasticity. [ABSTRACT FROM AUTHOR]

In this paper, we propose two decomposition dynamical systems for solving strongly pseudomonotone variational inequalities given by a sum of two mappings. We prove that trajectories of these dynamical systems converge to the unique solution of the variational inequality. Also, we extend these algorithms for equilibrium problems and study their convergence rate. This approach is novel and the new algorithms can be considered as continuous-time versions of existing decomposition algorithms for variational inequalities and equilibrium problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature. [ABSTRACT FROM AUTHOR]

The paper aims to introduce inverse tensor variational inequalities and analyze their application to an economic control equilibrium model. More precisely, some existence and uniqueness results are established and the well-posedness analysis is investigated. Moreover, the Tikhonov regularization method is extended to tensor inverse problems to study them when they are ill-posed. Lastly, the policymaker's point of view for the oligopolistic market equilibrium problem is introduced. The equivalence between the equilibrium conditions and a suitable inverse tensor variational inequality is established. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate a generalized type of mixed variational inequality (GMVI) in Banach space. Under the general assumptions, we first apply Minty's approach to deliver an equivalent result for GMVI and provide the existence condition of the solutions of GMVI. Then, the concepts of the strong and the weak well-posedness are introduced in the generalized sense, which are applied to discuss the essential relation between the metric characterizations and the generalized strong well-posedness as well as the weak well-posedness for GMVI. Moreover, the theorems are established to determine the generalized the strong and the weak well-posedness of GMVI, respectively. Furthermore, we consider a family of approximating problems corresponding to GMVI, which are dominated by the perturbation parameter ε, and a critical convergence result is obtained. Finally, an example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

This is the first paper dealing with the study of minimum and maximum principle sufficiency properties for nonsmooth variational inequalities by using gap functions in the setting of Hadamard manifolds. We also provide some characterizations of these two sufficiency properties. We conclude the paper with a discussion of the error bounds for nonsmooth variational inequalities in the setting of Hadamard manifolds. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

In this paper, weak sharp solutions are investigated for a class of variational-type inequalities involving curvilinear integral functionals. Moreover, by using the minimum principle sufficiency property, some characterization results on the weak sharpness property of the solution set for the considered class of variational-type inequalities are formulated and proved. Finally, in order to illustrate the main results, an application is provided. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we extend the nonlinear Lebesgue spaces from the setting of Hadamard spaces to the setting of p-uniformly convex metric spaces. Afterward, we establish some Δ-convergence and strong convergence theorems for a recently introduced class of generalized nonexpansive mappings in the setting of p-uniformly convex metric spaces. Furthermore, we employ the newly introduced JK-iteration process to approximate the fixed points of this class. Finally, we construct new examples of this class of mappings in the context of p-uniformly convex metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a modified Halpern-type proximal point algorithm which comprises a finite family of resolvents of mixed equilibrium problems and a finite family of k-demimetric mappings. We prove that the algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems, which is also a common fixed point of a finite family of k-demimetric mappings in a Hadamard space. Furthermore, we give a numerical example of our algorithm to show the applicability of our algorithm. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce a new class of parametric elliptical variational-hemivariational inequality problems together with parametric inverse problems. We show the existence of solution for parametric inverse problem and well-posedness of parametric elliptical variational-hemivariationl inequality problems. An implementation in nonlinear elasticity, we address the parametric inverse problem for a parametric frictional unilateral contact problem. [ABSTRACT FROM AUTHOR]

Recently, in [Tang GJ, Cen JX, Nguyen VT, et al. Differential variational-hemivariational inequalities: existence, uniqueness, stability, and convergence. J Fixed Point Appl. 2020; DOI: ],we studied a comprehensive system called differential variational-hemivar-iational inequality (DVHVI, for short) which is composed of a nonlinear evolution equation and a time-dependent variational-hemivariational inequality in Banach spaces. We have proved the existence, uniqueness, and stability of the solution in mild sense, as well as a surprising convergence result for DVHVI. However, to illustrate the applicability of those theoretical results in Tang et al., the present paper is devoted to explore a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem. [ABSTRACT FROM AUTHOR]

It was claimed in [Sadeqi, I.—Salehi Paydar, M.: A comparative study of Ky Fan hemicontinuity and Brezis pseudomonotonicity of mappings and existence results, J. Optim. Theory Appl. 165(2) (2015), 344–358] that the gradient of a convex Gâteaux differentiable function is Fanhemicontinuous. The aim of the present paper is to correct this implication by exemplifying for ∇ ‖ ⋅ ‖ in a Hilbert space. This goal was achieved by considering its domain to be scalarly-positive (see Definition 3). For a perturbation of a Fan-hemicontinuous operator with ∇ ‖ ⋅ ‖ , weak compactness for the set of solutions of the variational inequality problem is obtained. [ABSTRACT FROM AUTHOR]