the study of stability problems of functional equations was motivated by a question of s.m. ulam asked in 1940. the first result giving answer to this question is due to d.h. hyers. subsequently, his result was extended and generalized in several ways.we prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=ag(x)+bg(y)on restricted domain. namely, we show, under some weak natural...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. they belong to the general category of patch-based methods. particularly, each self-affine map is defined by one pair of patches in the image domain. by minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. almost all image process...

This note derives bounds on the length of the primal-dual affine scaling directions associated with a linearly constrained convex program satisfying the following conditions: 1) the problem has a solution satisfying strict complementarity, 2) the Hessian of the objective function satisfies a certain invariance property. We illustrate the usefulness of these bounds by establishing the superlinea...

the object of this paper is to establish certain generalized fractional integration and differentiation involving generalized mittag-leffler function defined by salim and faraj [25]. the considered generalized fractional calculus operators contain the appell's function $f_3$ [2, p.224] as kernel and are introduced by saigo and maeda [23]. the marichev-saigo-maeda fractional calculus operat...