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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 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]

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]

In this paper, we define a generalized resolvent operator involving a 풢 ⁢ (⋅ , ⋅) -co-monotone mapping for solving a generalized variational inclusion problem. We show that the resolvent operator under consideration is single-valued as well as Lipschitz continuous. An iterative algorithm is constructed to obtain the approximate solution of our problem. An example is provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb's law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlinear Volterra integral equation satisfied by the early exercise boundary of the American put option in the one-dimensional diffusion model for a stock price with constant interest rate and constant dividend yield and with a local volatility depending on the current time t and the current stock price S. In the classical Black–Sholes model for a stock price, Theorem 4.3 of [S. D. Jacka, Optimal stopping and the American put, Math. Finance 1 1991, 2, 1–14] states that if the family of integral equations (parametrized by the variable S) holds for all S ≤ b(t) with a candidate function b(t), then this b(t) must coincide with the American put early exercise boundary c(t). We generalize Peskir's result [G. Peskir, On the American option problem, Math. Finance 15 2005, 1, 169–181] to state that if the candidate function b(t) satisfies one particular integral equation (which corresponds to the upper limit S = b(t), then all other integral equations (corresponding to S, S ≤ b(t) will be automatically satisfied by the same function b(t). [ABSTRACT FROM AUTHOR]

We consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {𝓟n} of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality 𝓟n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed by a small parameter εn. The unique solvability of 𝓟 and, for each n ∈ ℕ, the solvability of its perturbed version 𝓟n, are guaranteed by an existence and uniqueness result obtained in literature. Denote by u the solution of Problem 𝓟 and, for each n ∈ ℕ, let un be a solution of Problem 𝓟n. The main result of this paper states the strong convergence of un → u in X, as n → ∞. We show that the main result extends a number of results previously obtained in the study of Problem 𝓟. Finally, we illustrate the use of our abstract results in the study of a mathematical model which describes the contact of an elastic body with a rigid-deformable foundation and provide the corresponding mechanical interpretations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of asymptotically demicontractive multivalued mappings and establish a strong convergence theorem of the modified Mann iteration to a common fixed point of a finite family of asymptotically demicontractive multivalued mappings in a complete CAT(0) space. We also give a numerical example of our iterative method to show its applicability. [ABSTRACT FROM AUTHOR]

In the present paper we investigate a three-dimensional boundary-contact problem of dynamics for a homogeneous hemitropic elastic medium with regard to friction. We prove the uniqueness theorem using the corresponding Green formulas and positive definiteness of the potential energy. To analyze the existence of solutions we reduce equivalently 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 Faedo-Galerkin 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]