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In this paper, we state some characterizations of h-convex function defined on a convex set in a linear space. By doing so, we extend the Jensen–Mercer inequality for h-convex function. We present the concept of operator h-convex functions and give some operator versions of Jensen and Jensen–Mercer type inequalities for some classes of operator h-convex functions and unital positive linear maps. Finally, we introduce the complementary inequality of Jensen's inequality for h-convex functions. [ABSTRACT FROM AUTHOR]

The present paper deals with the theory of duality for the Mayer problem given by second-order polyhedral discrete and differential inclusions. First, we formulate the conditions of optimality in the form of Euler–Lagrange type inclusions and transversality conditions for the polyhedral problems with second-order discrete and differential inclusions. Second, we establish dual problems for discrete and differential inclusions based on the infimal convolution concept of convex functions and prove the results of duality. For both primary and dual problems, the Euler–Lagrange type inclusions are "duality relations" and that the dual problem for discrete-approximate problems bridges the gap between the dual problems of discrete and continuous problems. As a result, the passage to the limit in the dual problem with discrete approximations plays a substantial role in the following investigations, without any which can hardly ever be established by any duality to the continuous problem. Furthermore, the numerical results also are provided. [ABSTRACT FROM AUTHOR]

In this paper, we determine the radii of β -uniform convexity of order α for six kinds of normalized Lommel and Struve functions of the first kind. One of the most important things which we have learned in this study is that the radii of uniform convexity are obtained as solutions of some transcendental equations. [ABSTRACT FROM AUTHOR]

The theory of (j, k)-symmetric functions has many applications in the investigation of fixed points, estimation of the absolute values of some integrals and in obtaining results of the type of Cartan’s uniqueness theorem. The concept of 2j,k-symmetric functions extends the idea of even, odd, k, 2k,  j,k-symmetric and conjugate functions. In this paper, we introduce a new class MSCPj,kα,η,δ of analytic functions using the notion of 2j,k-symmetric conjugate points. It unifies the classes SSCPj,kη,δ and CSCPj,kη,δ of starlike functions with respect to symmetric conjugate points and convex functions with respect to symmetric conjugate points, respectively. We also derive some inclusion results, integral representations and convolution conditions for functions belonging to the general function class MSCPj,kα,η,δ. The various results presented in this paper may apply to yield the corresponding (new or known) results for a number of simpler known classes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new customized proximal point algorithm for linearly constrained convex optimization problem, and further extend the proposed method to separable convex optimization problem. Unlike the existing customized proximal point algorithms, the proposed algorithms do not involve relaxation step, but still ensure the convergence. We obtain the particular iteration schemes and the unified variational inequality perspective. The global convergence and O (1 / k) -convergence rate of the proposed methods are investigated under some mild assumptions. Numerical experiments show that compared to some state-of-the-art methods, the proposed methods are effective. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some Jensen’s and Hermite-Hadamard’s type inequalities for lower, upper, and strongly convex functions defined on convex subsets in normed linear spaces. The case of inner product space is of interest since in these case the concepts of lower convexity and strong convexity coincides. Applications for univariate functions of real variable and the connections with earlier Hermite-Hadamard’s type inequalities are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two positive semidefinite matrices A and B we show that ‖AνXB1-ν+A1-νXBν‖22≤‖AX+XB‖22-2r‖AX-XB‖22-r0‖A12XB12-AX‖22+‖A12XB12-XB‖22,where X is an arbitrary n×n matrix, 0<ν≤12, r=min{ν,1-ν} and r0=min{2r,1-2r}. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general integral operator Gn(z): The main object of the present paper is to study some properties of this integral operator on the classes S*(α), K(α), M(β), N(β) and KD(μ,β). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a subclass of close-to-convex functions defined in the open unit disk. We obtain the inclusion relationships, coefficient estimates and the Fekete-Szegö inequality. The results presented here would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the proximal point algorithm to complete CAT(0) spaces and show that the sequence generated by the proximal point algorithm w-converges to a zero of the maximal mono-tone operator. Also, we prove that if f : X →] - ∞, +∞] is a proper, convex and lower semicontinuous function on the complete CAT(0) space f, then the proximal point algorithm w-converges to a zero of the sub-differential of f, i.e., a minimizer of f. Some strong convergence results (convergence in metric) are also presented with additional assumptions on the monotone operator and the convex function f. [ABSTRACT FROM AUTHOR]

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Ba- nach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover, we prove some weak con- vergence theorems for such mappings by using Ishikawa iteration method in a uniformly convex Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish some extended Simpson-type inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Simpson formula are also given. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and sufficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spaces is addressed and some basic properties are highlighted. Finally, a density theorem for subdifferential set is established. [ABSTRACT FROM AUTHOR]

Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we define a subclass Tp(a, c, γ, λ, h) of meromorphically multivalent functions. The main object of this paper is to investigate some important properties for the class. We also derive many results for the Hadamard products of functions belonging to the class. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new classTs;ak[A, B, α, β] of analytic functions by using a newly defined convolution operator. This class contains many known classes of analytic and univalent functions as special cases. We derived some interesting results including inclusion relationships, a radius problem and sharp coefficient bound for this class. [ABSTRACT FROM AUTHOR]

In a real Hilbert space, an iterative scheme is considered to obtain strong convergence which is an essential tool to find a common fixed point for a countable family of nonexpansive map- pings and the solution of a variational inequality problem governed by a monotone mapping. In this paper, we give a procedure which results in developing Shehu's result to solve equilibrium problem. Then, we state more applications of this procedure. Finally, we investigate some numerical examples which hold in our main results. [ABSTRACT FROM AUTHOR]