We define a class of L-convex-concave subsets of RP , where L is a projective line in RP . These are sets whose sections by any plane containing L are convex and concavely depend on this plane. We prove a version of Arnold’s conjecture for these sets, namely we prove that each such set contains a line.

We define a class of L-convex-concave subsets of RP 3 , where L is a projective line in RP 3. These are sets whose sections by any plane containing L are convex and concavely depend on this plane. We prove a version of Arnold hypothesis for these sets, namely we prove that each such set contains a line.

The total variation (TV) measure is a key concept in the field of variational image analysis. Introduced by Rudin, Osher and Fatemi in connection with image denoising, it also provides the basis for convex structure-texture decompositions of image signals, image inpainting, and for globally optimal binary image segmentation by convex functional minimization. Concerning vector-valued image data,...

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].