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This paper is devoted to numerical analysis of a new class of elliptic variational–hemivariational inequalities in the study of a family of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modeled by a nonmonotone multivalued subdifferential relation allowing slip dependence. The problem involves a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set for the locking constraints and a nonconvex locally Lipschitz friction potential. Solution existence and uniqueness result on the inequality can be found in Migórski and Ogorzaly (2017). In this paper, we introduce and analyze a finite element method to solve the variational–hemivariational inequality. We derive a Céa type inequality that serves as a starting point of error estimation. Numerical results are reported, showing the performance of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper, we derive the time-fractional Cahn–Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze the existence, uniqueness, and regularity of weak solutions of the time-fractional Cahn–Hilliard equation. In this regard, we consider degenerating mobility functions and free energies of Landau, Flory–Huggins and double-obstacle type. We apply the Faedo–Galerkin method to the system, derive energy estimates, and use compactness theorems to pass to the limit in the discrete form. In order to compensate for the missing chain rule of fractional derivatives, we prove a fractional chain inequality for semiconvex functions. The work concludes with numerical simulations and a sensitivity analysis showing the influence of the fractional power. Here, we consider a convolution quadrature scheme for the time-fractional component, and use a mixed finite element method for the space discretization. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points in , the barycentric approximation of a convex function is of the form: where is a set of barycentric coordinates with respect to the point set . The main content of this paper is two-fold. The first goal is to derive sharp upper and lower bounds on all barycentric coordinates over the convex polytope . The second objective of the paper is to exploit the convexity assumption heavily and establish a number of upper and lower pointwise bounds on the approximation error for approximating arbitrary convex functions. These bounds depend solely on computable quantities related to the data values of the function, the largest and smallest barycentric coordinates. For convex twice continuously differentiable functions, we derive an optimal error estimate. We show that the Delaunay triangulation gives access to efficient algorithms for computing optimal barycentric approximation. Finally, numerical examples are used to show the success of the method. [Copyright &y& Elsevier]

Abstract In this paper, a new total generalized variational(TGV) model for restoring images with multiplicative noise is proposed, which contains a nonconvex fidelity term and a TGV term. We use a difference of convex functions algorithm (DCA) to deal with the proposed model. For multiplicative noise removal, there exist many models and algorithms, most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Unlike these algorithms, we use the DCA algorithm to remove multiplicative noise. By numerical experiments, it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models. We prove that the sequence generated by the DCA algorithm converges to a stationary point, which satisfies the first order optimality condition. Finally, we demonstrate the performance of our whole scheme by numerical examples. A comparison with other methods is provided as well. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative Gamma noise removal. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new class of functions analytic in the open unit disc, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well known classes. The paper deals with several ideas and techniques used in geometric function theory. The order of starlikeness in the class of convex functions of negative order is also considered here. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some Hermite–Hadamard-type inequalities for convex functions and give several applications for special means. They complete the results from the previous recent paper Tseng et al. (submitted for publication) . [Copyright &y& Elsevier]

Abstract: The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain. [Copyright &y& Elsevier]

Abstract: In the present paper we establish several differential superordinations regarding the new operator defined by using the generalized Sălăgean operator and Ruscheweyh derivative , , where , and , A number of interesting consequences of some of these superordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. [Copyright &y& Elsevier]

Most of local region-based active contour models in terms of the level set approach are able to segment images with intensity inhomogeneity. However, these models do not utilize global statistical information and are quite sensitive to the initial placement of the contour. This paper presents a new global and local region-based active contour model to segment images with intensity inhomogeneity. First, in order to reduce number of iterations, the global energy functional of the Chan–Vese (C–V) model is used as the global term. Then, the local term is proposed to incorporate both local spatial information and local intensity information to handle intensity inhomogeneity. Moreover, to increase robustness of the initialization of the contour and reduce number of iterations, a convex energy functional and the dual algorithm are designed in the numerical implementation. Experimental results for synthetic and medical images have shown the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a fast multiphase image segmentation model for gray images. Our proposed model is based on the piecewise constant multiphase Vese–Chan model, the globally convex segmentation method and the split Bregman method. Our proposed model has the advantages of the Vese–Chan model and can deal with piecewise constant multiphase images well. Besides, our proposed model is much more efficient than the Vese–Chan model by applying the globally convex segmentation method and the split Bregman method. We have tested our proposed model with many synthetic and real images. Experimental results have demonstrated the efficiency and robustness of our proposed model. [Copyright &y& Elsevier]

Abstract: In this paper, we shall establish some Hadamard-type and Bullen-type inequalities for Lipschitzian functions and give several applications for special means. [Copyright &y& Elsevier]

Abstract: In this paper, the Hardy–Littlewood–Pólya theorem on majorization is extended from convex functions to invex ones. Some variants for pseudo-invex and quasi-invex functions are also considered. The framework used is that of similarly separable vectors. The results obtained are illustrated for monotonic, monotonic in mean, and star-shaped vectors, respectively. Applications to relative invexity are given. [Copyright &y& Elsevier]

Abstract: Let , , denote the class of all normalized analytic functions in the unit disc such that for some . Let , , denote the Pascu class of -convex functions of order and given by the analytic condition which unifies and , respectively, the classes of analytic functions that map onto the starlike and convex domain. In this work, we consider integral transforms of the form The aim of this paper is to find conditions on so that the above transformation carry into . As applications, for specific values of , it is found that several known integral operators carry into . [Copyright &y& Elsevier]

Abstract: In this paper, some properties of log-convex function are researched, and integral inequalities of log-convex functions are proved. As an application, an estimation formula of remainder terms in Taylor series expansion is given. [Copyright &y& Elsevier]

Abstract: Antczak introduced vector-valued -invex functions in 2009, which is a new class of generalized convex functions for differentiable multiobjective programming problems. In this paper, we extend the vector-valued -invex functions to multiobjective variational control problems. By using the new concepts, a number of sufficient optimality results and Mond–Weir type duality results are obtained for multiobjective variational control programming problems. [Copyright &y& Elsevier]

Abstract: In this paper, by using Jensen’s inequality and Hadamard’s integral inequality for a convex function, some generalizations and improvements of discrete Hardy’s inequality and Carleman’s inequality are obtained. [Copyright &y& Elsevier]

Abstract: In this paper we consider the classes of -uniformly convex and -starlike functions defined in Kanas and Wiśniowska (1999, 2000)  which generalize the class of uniformly convex functions introduced by Goodman (1991) . We discuss the real part of , when is -starlike. We find the minimum of improving the results obtained recently in Wiśniowska-Wajnryb (2009) . [Copyright &y& Elsevier]

Abstract: In this paper, we find conditions on the coefficients such that the corresponding trigonometric (cosine and sine) sums given respectively by and for all are positive. Using these results, we find that the functions that are in the class of analytic functions are starlike of certain order in the unit disc by means of conditions on the Taylor coefficients of . As an application, we also find conditions such that the Cesáro means of order of are close-to-convex and starlike in . [Copyright &y& Elsevier]

Abstract: This paper deals with the optimization of keloid surgery strategies. The phenomenological interpretation of the medical/biological system under consideration leads to the modeling of the growth of a keloid and to the assessment of an objective functional, the minimization of which identifies the aforesaid strategy. [Copyright &y& Elsevier]

Abstract: In this paper, the concepts of Janowski functions and the conic regions are combined to define a new domain which represents the conic type regions. Different views of this modified conic domain for specific values are shown graphically for better understanding of the behavior of this domain. The class of such functions which map the open unit disk onto this modified conic domain is defined. Also the classes of -uniformly Janowski convex and -Janowski starlike functions are defined and their coefficient inequalities are formulated. The coefficient bound for a certain class of analytic functions, proved by Owa et al. (2006) in , has also been improved. [Copyright &y& Elsevier]

Abstract: This paper investigates some basic geometric properties for the class of functions analytic in the open unit disc (which is related to a shell-like curve and associated with Fibonacci numbers) satisfying the condition that where, the number is such that fulfils the golden section of the segment . Some relevant remarks and useful connections of the main results are also pointed out. [Copyright &y& Elsevier]

Abstract: In this paper, we establish several new inequalities for functions whose second derivative in absolute value aroused to the power are -convex. Some applications to special means of positive real numbers are also given. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some new inequalities of Simpson’s type based on -convexity. Some applications to special means of real numbers are also given. [Copyright &y& Elsevier]

Abstract: This paper presents a procedure for finding the optimal replenishment and production schedule for a single-vendor single-buyer inventory model and where the objective is to minimize the total integrated inventory costs of the vendor and the buyer over one production schedule and a finite-planning horizon. The production rate of the vendor is assumed fixed and the demand rate of the buyer is assumed to take some general form and is a function of time. It is shown that for a fixed number of replenishment schedules, , the optimal times of ordering are unique and can be found as a solution of some system of nonlinear equations. These in turn give the optimal order quantities of the buyer in each period. Moreover, the optimal value function is shown to be convex in . [Copyright &y& Elsevier]

Abstract: We investigate several properties of the linear Aouf–Silverman–Srivastava operator and associated classes of multivalent analytic functions which were introduced and studied by Aouf et al. [M.K. Aouf, H. Silverman, H.M. Srivastava, Some families of linear operators associated with certain subclasses of multivalent functions, Comp. Math. Appl. 55 (2008) 535–549]. Several theorems are extensions of earlier results of the above paper. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, the authors investigate starlikeness and convexity of a class of multivalent functions defined by an extended multiplier transformation. As a consequence, a number of sufficient conditions for starlikeness and convexity of analytic functions are also obtained. [Copyright &y& Elsevier]

Abstract: The main aim of the present paper is to survey different inequalities for convex functions of selfadjoint operators in Hilbert spaces which have appeared recently in the literature. Applications for some particular convex functions of interest are also given. [Copyright &y& Elsevier]

Abstract: The objective of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions of order type . We also consider an integral operator related to the hypergeometric function. [Copyright &y& Elsevier]

Abstract: The main result in this paper is to establish some new characterizations of convex functions, in which we also simplify the proof of the characterizations given by Bessenyei and Páles. [Copyright &y& Elsevier]

Abstract: In this paper, some inequalities of Hadamard’s type for quasi-convex functions are given. Some error estimates for the Trapezoidal formula are obtained. Applications to some special means are considered. [Copyright &y& Elsevier]

Abstract: In this paper we prove the Hermite–Hadamard–Fejér inequalities for an -convex function and we point out the results for some special classes of functions. Also, some generalization of the Hermite–Hadamard inequalities and some properties of functions and which are naturally joined to the -convex function are given. Finally, applications on -logarithmic mean and mean of the order are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and investigate two new classes of meromorphic multivalent functions. Such results as subordination properties, coefficient inequalities, convolution properties and integral representations are proved. Several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived. [Copyright &y& Elsevier]

Abstract: The purpose of the present paper is to derive some differential inequalities for certain analytic functions in the open unit disk by appealing to a result obtained by the first author. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [Copyright &y& Elsevier]

Abstract: For analytic functions in the open unit disk and convex functions in , Ch. Pommerenke [Ch. Pommerenke, On close-to-convex analytic functions, Trans. Amer. Math. Soc. 114 (1) (1965) 176–186] has proved one theorem which is a generalization of the result by K. Sakaguchi [K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959) 72–75]. The object of the present paper is to generalize the theorem due to Pommerenke. [Copyright &y& Elsevier]

Abstract: In this paper, by applying Jensen’s inequality for convex functions, a generalization of the Ky Fan discrete multivariate inequality is obtained and some of its applications are also given. [Copyright &y& Elsevier]

Abstract: This paper concerns a nonmonotone line search technique and its application to the trust region method for unconstrained optimization problems. In our line search technique, the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value, instead of an average of the successive objective function values that was introduced by Zhang and Hager [H. Zhang, W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14 (4) (2004) 1043–1056]. We incorporate this nonmonotone scheme into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the traditional trust region method, our algorithm performs a nonmonotone line search to find a new iteration point if a trial step is not accepted, instead of resolving the subproblem. Under mild conditions, we prove that the algorithm is global and superlinear convergence holds. Primary numerical results are reported. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to introduce and study an idea of strong double -convergence sequences with respect to an Orlicz function. In addition, we define the double -statistical convergence and establish some connections between the spaces of strong double -convergence sequences and the space of double -statistical convergence. [Copyright &y& Elsevier]

Abstract: In this paper, we prove some properties of the generalized -projection operator in Banach spaces and show an interesting relation between the generalized -projection operator and the resolvent operator for the subdifferential of a proper, convex and lower semi-continuous functional in reflexive and smooth Banach spaces. Moreover, we prove that the generalized -projection operator is maximal monotone. As applications, we propose an iterative method of approximating solutions for a class of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces. [Copyright &y& Elsevier]

We introduce three-step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes. Mann-type and Ishikawa-type convergence results are included in the analysis of these new iteration schemes. The results presented in this paper substantially improve and extend the results due to [S.H. Khan, H. Fukhar-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal. 8 (2005) 1295–1301], [N. Shahzad, Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear Anal. 61 (2005) 1031–1039], [W. Takahashi, T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Anal. 5 (1995) 45–58], [K.K. Tan, H.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993) 301–308] and [H.F. Senter, W.G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974) 375–380]. [Copyright &y& Elsevier]

Abstract: In this paper, a criterion for the convex fuzzy mapping is obtained under the condition of upper and lower semicontinuity, respectively. An upper (lower) semicontinuous fuzzy mapping is proved, which convexity is equivalent to weak convexity or B-vexity satisfying a special condition. [Copyright &y& Elsevier]

Abstract: In, we have developed generalized quasilinearization method for reaction diffusion systems when the forcing functions are the sum of convex and concave functions. The solutions of the corresponding linear systems converge monotonically, uniformly and quadratically to the unique solution of the nonlinear problem. As a byproduct of our result, we have discussed the reaction diffusion system when the forcing function satisfies mixed quasimonotone property. In this paper, we have established the application of the theoretical results developed in with numerical examples. We also demonstrate the consistency of the finite different scheme and discuss the stability and convergence of the scheme for the examples considered here. [Copyright &y& Elsevier]

Abstract: By making use of certain familiar integral operators, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex functions. Among other results presented here, the authors establish a number of inclusion relationships associated with some of these integral operators. Some of the results established in this paper would provide extensions of those given in earlier works. [Copyright &y& Elsevier]

Abstract: Semi-definite programs are convex optimization problems arising in a wide variety of applications and the extension of linear programming. Most methods for linear programming have been generalized to semi-definite programs. This paper discusses the discretization method in semi-definite programming. The convergence and the convergent rate of error between the optimal value of the semi-definite programming problems and the optimal value of the discretized problems are obtained. An approximately optimal division is given under certain assumptions. With the significance of the convergence property, the duality result in semi-definite programs is proved in a simple way which is different from the other common proofs. [Copyright &y& Elsevier]

Abstract: By making use of the familiar concept of neighborhoods of analytic and p-valent functions, the authors prove coefficient bounds and distortion inequalities, and associated inclusion relations for the (n, δ)-neighborhoods of a family of multivalent functions with negative coefficients, which is defined by means of a certain nonhomogeneous Cauchy-Euler differential equation. Relevant connections of the various function classes investigated in this paper with those considered by earlier workers on the subject are also mentioned. [Copyright &y& Elsevier]

In this paper, we present numerous sets of nonparametric sufficient optimality conditions and duality results under various generalized (F ϱ, θ)-convexity assumptions for a minmax fractional subset programming problem. [Copyright &y& Elsevier]

In this paper, we first introduce a new class of generalized convex n-set functions, called (Ϝ, α, ϱ, θ)-V-convex functions, and then present numerous sets of parametric and semiparametric sufficient efficiency conditions under generalized (Ϝ, α, ϱ, θ)-V-convexity assumptions for a multiobjective fractional subset programming problem. Moreover, we construct three parametric and three semiparametric duality models and prove appropriate duality theorems. [Copyright &y& Elsevier]

Abstract: In this paper the authors prove some properties for two general integral operators on the classes and . [ABSTRACT FROM AUTHOR]