Convex like properties, without vector space structure are intensively used in the minimax theory Since Ky Fan has proved the first minimax theorem for concave-convexlike functions, several authors have proposed other extensions or generalizations for the convexity. In this paper we propose a survey of the recent studies concerning convexity and invexity in optimization theory. In fact, in the ...

In this article we examine to necessary and sufficient optimality conditions for interval optimization problems. We introduce a new concept of stationary point for an interval-valued function based on the gH-derivative. We show the importance the this concept from a practical and computational point of view. We introduce a new concept of invexity for gH-differentiable interval-valued function w...

In this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, consider Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, Pachpatte-type inequalities. We estimate inequalities for newly introduced class ?-preinvexity over fuzzy-number valued settings. For first time, such involving functions are proven u...

The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

OBJECTIVE This study evaluated the influence of low concentration acid treatment on the shear bond strength between lithium disilicate (LD) infrastructure and veneering porcelain. The surface morphology characteristic after this acid treatment was also examined. STUDY DESIGN LD reinforced ceramic cylinders (n=10) (IPS e.max Press, Ivoclar-Vivadent, Schaan, Liechtenstein) were treated (LD-trea...

Given a model M and a temporal logic formula φ[?], where ? is a placeholder, the query checking problem, as defined for the case of CTL by Chan in 2000, is to find the strongest propositional formula f such that M |= φ[? ← f ]. The motivation for solving this problem is, among other things, to get insight on the model. We consider various objectives to the LTL query-checking problem, and study ...