In this paper, we point out that the proof of Theorem 2.4(5), Proposition 2.6(1) and 2.8(1) in paper titled ?On (L,M)-fuzzy convex structures? (Filomat 33(13): 4151-4163, 2019) are not true general. Then, give three correct proofs these results

We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an “L” shaped path in one of its four cyclic orientations. The paper proves bijectively that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the linear recurrence relation fn+2 = 4 fn+1 − 2 fn , by first establishing a recurrence of the same form for the car...

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called flow tents. This allows us to establish weighted norm estimates for Bergman projection P such with respect Muckenhoupt weights. particular, result gives an alternative proof $$L^p$$ boundedness P. Moreover, using extrapolation, are also able derive vector-valued and modular inequalities projection.

Our main purpose is to characterize the class of L-convex polyominoes introduced in [3] by means of their horizontal and vertical projections. The achieved results allow an answer to one of the most relevant questions in tomography i.e. the uniqueness of discrete sets, with respect to their horizontal and vertical projections. In this paper, by giving a characterization of L-convex polyominoes,...

In 1949 Horn and Valentine [HV] showed that if each pair of points a,b in a simple polygon P could be connected by a polygonal path of length two lying in P (such polygons are termed L-convex polygons) then through each point x in P there exists a line segment L(x) lying in P such that for every point y in P there exists a point z in L(x) with the property that the segment yz lies in P. Since t...

The present knowledge about L-convex and M-convex functions are surveyed on the basis of [27].

If a convex body K in R is contained in a convex body L of elliptic type (a curvature image), then it is known that the affine surface area of K is not larger than the affine surface area of L. We prove that the affine surface areas of K and L can only be equal if K = L. 2010 Mathematics Subject Classification: primary 52A10; secondary 53A15

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

which is still the best known estimate for arbitrary convex bodies. Another class consists of convex bodies with small volume ratio with respect to the ellipsoid of minimal volume. This includes the class of zonoids. K. Ball [BA] solved the problem for the duals of zonoids, i.e. unit balls of subspaces of an L1-space, briefly L1-sections. Theorem 1 (K. Ball) For a convex, symmetric body K ⊂ IR ...