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

DOI

10.3906/mat-1606-51

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

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