In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

1. L’Hôpital’s Rule 1 1.1. The Cauchy Mean Value Theorem 1 1.2. L’Hôpital’s Rule 2 2. Newton’s Method 5 2.1. Introducing Newton’s Method 5 2.2. A Babylonian Algorithm 6 2.3. Questioning Newton’s Method 7 2.4. Introducing Infinite Sequences 7 2.5. Contractions and Fixed Points 8 2.6. Convergence of Newton’s Method 10 2.7. Quadratic Convergence of Newton’s Method 11 2.8. An example of nonconverge...

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

We introduce the class of (k,h) -convex functions defined on k -convex domains, and we prove some new inequalities of Hermite-Hadamard and Fejér type for such mappings. This generalizes results given for h -convex functions in [1, 17], and for s -Orlicz convex mappings in [4]. Mathematics subject classification (2010): Primary: 26A51, 26D15; Secondary: 52A30.

The alternating direction method of multipliers (ADMM) is widely used in solving structured convex optimization problems. Despite of its success in practice, the convergence properties of the standard ADMM for minimizing the sum of N (N ≥ 3) convex functions with N block variables linked by linear constraints, have remained unclear for a very long time. In this paper, we present convergence and...

Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

Contents 1 The basic concepts 1 1.1 Is convexity useful? 1 1.2 Nonnegative vectors 4 1.3 Linear programming 5 1.4 Convex sets, cones and polyhedra 6 1.5 Linear algebra and affine sets 11 1.6 Exercises 14 2 Convex hulls and Carathéodory's theorem 17 2.1 Convex and nonnegative combinations 17 2.2 The convex hull 19 2.3 Affine independence and dimension 22 2.4 Convex sets and topology 24 2.5 Carat...