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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 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: 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: 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]