The Q-convexity is a kind of convexity in the discrete plane. This notion has practically the same properties as the usual convexity: an intersection of two Qconvex sets is Q-convex, and the salient points can be defined like the extremal points. Moreover a Q-convex set is characterized by its salient point. The salient points can be generalized to any finite subset of Z2.

In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in infinite dimensional settings and use the connections in order to obtain improved convergence results concerning...

In this article, we define a new class of convexity called generalized $(h-m)$-convexity, which generalizes $h$-convexity and $m$-convexity on fractal sets $\mathbb{R}^{\alpha}$ $(0<\alpha\leq 1)$. Some properties are discussed. Using local fractional integrals Hermite-Hadamard (H-H) Fej\'er-Hermite-Hadamard (Fej\'er-H-H) types inequalities. We also obtained result the Fej\'er-H-H type for func...

In this paper, we introduce general classes of generalized monotonicity and generalized convexity. For each type of (relatively) generalized monotone map, we establish a relationship to (relatively) generalized convex function. In this way, we obtain first-order characterizations for various (relatively) generalized convex functions. Our results extend/generalize similar result obtained in [3].

The paper aims to emphasise the parallelism between the development of the analysis of Generalized Convexity and the theory of Variational Inequalities. More in detail, the relationships between generalized invexity and Prevariational Inequalities are analised.

We use the ideas of generalized convexity. We focus our attention on the set of multipliers. We look for an interpretation of multipliers as generalized derivatives of the performance function associated with a dualizing parameterization of the given problem.

The Wright’s generalized hypergeometric function is used here to introduce a new class of p-valent functions WT p(λ, α, β) defined in the open unit disc and investigate its various characteristics. Further we obtain distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity of functions belonging to the class WT p(λ, α, β).

In this paper, we consider a more general form of generalized nonlinear variational inclusions and prove the existence of solutions for these generalized nonlinear variational inclusions with and without convexity.

The generalized trigonometric functions which have a short history, were introduced by Lindqvist two decades ago. Since 2010, many mathematician began to study their classical inequalities, general convexity and concavity, multiple-angle formulas and parameter convexity and concavity. A number of results have been obtained. This is a survey. Some new refinements, generalizations, applications, ...

in the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{kim} and textit{lee} [w.k. kim and k.h. lee, generalized fuzzy games and fuzzy equilibria, fuzzy sets and systems, 122 (2001), 293-301] and textit{tarafdar} [e. tarafdar, fixed point theorems i...