If $4$-convex vectors are closed in uniform norms then their second derivatives are also closed in weighted $L^2$-norm

Authors

MUHAMMAD SHOAIB SALEEM
JOSIP PECARIC
HAMOOD UR REHMAN
MOBEEN MUNIR
MUHAMMAD WAHAB KHAN

Abstract

In this paper, we develop the weighted energy estimates for arbitrary 4-convex vectors and the vectors having both 4-convex and 4-concave functions as their arguments. To do this, we first develop these estimates for smooth 4-convex vectors and then, through mollification, extend the results for arbitrary 4-convex vectors. This type of estimates are valuable in problems of financial mathematics for the establishment of optimal investment strategies

DOI

10.3906/mat-1606-51

Keywords

Smooth convex vectors, smooth concave vectors, vector convolution

First Page

2091

Last Page

2100

Recommended Citation

SALEEM, MUHAMMAD SHOAIB; PECARIC, JOSIP; REHMAN, HAMOOD UR; MUNIR, MOBEEN; and KHAN, MUHAMMAD WAHAB (2018) "If $4$-convex vectors are closed in uniform norms then their second derivatives are also closed in weighted $L^2$-norm," Turkish Journal of Mathematics: Vol. 42: No. 5, Article 2. https://doi.org/10.3906/mat-1606-51
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/2