It is the purpose of this paper to propose a novel class convex functions associated with strong ?-convexity. A relationship between newly defined function and an earlier generalized hereby established. To point out importance new functions, some examples are presented. Additionally, famous Hermite–Hadamard inequality derived for family functions. Furthermore, inequalities results ?-convex also...

Attouch's Theorem, which gives on a reflexive Banach space the equivalence between the Mosco epi-convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients, has many important applications in convex optimization. In particular, generalized derivatives have been defined in terms of the epi-convergence or graph convergence of certain differe...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

This paper presents an overview of the research progress in global optimization during the last 5 years (1998–2003), and a brief account of our recent research contributions. The review part covers the areas of (a) twice continuously differentiable nonlinear optimization, (b) mixedinteger nonlinear optimization, (c) optimization with differential-algebraic models, (d) optimization with grey-box...

In this paper, we investigate several inclusion relationships of certain subclasses of meromorphically p-valent functions which are defined here by means of a linear operator involving the generalized hypergeometric function . We introduce and investigate several new subclasses of p-valent starlike, p-valent convex, p-valent close-to-convex and p-valent quasiconvex meromorphic functions.