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Abstract: In the present paper, we introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, distortion property and radius of meromorphic convexity are derived. [Copyright &y& Elsevier]

Abstract: The aim of this note is to give an alternative proof for a recent result due to Dorsch et al., which provides an upper estimate for the Clarke subdifferential of an infimal value function. We show the validity of this result under a weaker condition than the one assumed in the aforementioned paper, while the use of the Mordukhovich subdifferential, as an intermediate step, will considerably shorten its proof. [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 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 define and study some subclasses of analytic functions by using fractional derivative operator. Some interesting properties, coefficients problems and inclusion results of these classes are investigated. It is also shown that these classes are closed under convolution with convex functions and some applications are given. [Copyright &y& Elsevier]

Abstract: In the present paper, we give a growth theorem of Bazilevič functions of type (α, β). [Copyright &y& Elsevier]

Abstract: In this paper, alternative proofs are provided for monotonic and logarithmically convex properties of the one-parameter mean values and for monotonic properties of the product on . [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]

Abstract: An interesting criterion was given by Tuneski [N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248–249 (2003) 200–203] for the analytic functions to be in the class and its subclasses, where . This result is an extension of an earlier result of Silverman [H. Silverman, Convex and starlike criteria, Int. Math. Math. Sci. 22 (1) (1999) 75–79] for α-starlike functions. In this paper we give a generalization of main theorem contained in Tuneski (2003). Some applications involving this result are also considered. [Copyright &y& Elsevier]

Abstract: The main object of the present paper is to investigate α-convex and α-quasiconvex functions with respect to n-symmetric points. Some interesting properties such as inclusion relationships, integral representations, convolution conditions are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we study the following degenerate parabolic problem: where is a continuous function which could be negative in a bounded set of and a convex increasing function. Under additive conditions, we prove the uniqueness of the positive stationary solution and, then, give the asymptotic behaviour of solutions to when . [Copyright &y& Elsevier]

Abstract: Let be a set of points in in general position such that each point is coloured with one of colours. An alternating path of is a simple polygonal whose edges are straight line segments joining pairs of elements of with different colours. In this paper we prove the following: suppose that each colour class has cardinality and is the set of vertices of a convex polygon. Then always has an alternating path with at least elements. Our bound is asymptotically sharp for odd values of . [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: The method of successive averages is often used in iterative algorithms for solving various mathematical problems, and travel forecasting models in particular. In each iteration of these algorithms the current solution is averaged with an alternative solution generated by the algorithm. If the problem has an equivalent convex optimization formulation with a computable objective function, a line search can be used to determine the weight applied to the alternative solution, referred to as the step size. In the absence of a convex optimization formulation, the typical approach is to set the step size according to a predetermined sequence that is decreasing towards zero, such as 1/k where k is the iteration index. In this paper, we examine the use of a constant step size in the method of successive averages. A theoretical derivation shows that if the alternative solution generated by the algorithm is a linear function of the current solution, then using a constant step size is advantageous and substantially superior to using a sequence of decreasing step sizes. We conjecture that similar results may be expected in nonlinear differentiable problems as well. Numerical results are presented for a travel forecasting model that combines user-equilibrium route choice with an origin-destination-mode (ODM) choice model. The proposed algorithm is based on origin-based assignment, in conjunction with successive averaging of constant step sizes for the differentiable ODM model. The results show that a properly chosen constant step size leads to excellent convergence for both convex and non-convex models. A general strategy for choosing step sizes without a-priori knowledge is presented as well. [Copyright &y& Elsevier]

Abstract: In the theory of two-sided matching markets there are two standard models: (i) the marriage model due to Gale and Shapley and (ii) the assignment model due to Shapley and Shubik. Recently, Eriksson and Karlander introduced a hybrid model, which was further generalized by Sotomayor. In this paper, we propose a common generalization of these models by utilizing the framework of discrete convex analysis introduced by Murota, and verify the existence of a pairwise-stable outcome in our general model. [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]

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]