We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weirtype dual problems for our nonsmo...

This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the...

Correspondence: gaoyingimu@163. com Department of Mathematics, Chongqing Normal University, Chongqing 400047, China Abstract In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second or...

In this paper, we consider a very useful and significant class of convex sets and convex functions that is relative convex sets and relative convex functions which was introduced and studied by Noor [20]. Several new inequalities of Hermite-Hadamard type for relative convex functions are established using different approaches. We also introduce relative h-convex functions and is shown that rela...

Making use of generalized integral operator, we define a subclass of analytic functions with negative coefficients. The main object of this paper is to obtain coefficient estimates, closure theorems and extreme points. Also we obtain radii of close-to-convexity, starlikeness and convexity and neighbourhood results for functions in the generalized classR∗(α, β, μ, η). 2000 Mathematics Subject Cl...

Convexity spaces defined in the paper are generated by families of continuous functions. Without imposing any explicitly stated linear structure on the spaces, Browder’s, Brouwer’s and Kakutani’s fixed point theorems are proved and used for deriving generalized Fan inequalities and two-function minimax theorems. The existence of Nash equilibria in noncooperative games is also established under ...

Binayak et al in [1] proved a fixed point of generalized Kannan type-mappings in generalized Menger spaces. In this paper we extend gen- eralized Kannan-type mappings in generalized fuzzy metric spaces. Then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. Finally we present an example of our main result.

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.