Abstract In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to single equation. Applying fixed point theorem, study generalized Hyers–Ulam stability mappings. As result, investigate hyperstability mappings in some senses.

In this paper, we investigate the Hyers-Ulam stability of the orthogonally  cubic equation and  Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the  $2$-variables cubic  equation [ f(2x+y,2z+t)+f(2x-y,2z-t) =2...

We establish some stability results concerning the general cubic functional equation f(x+ ky)− kf(x+ y) + kf(x− y)− f(x− ky) = 2k(k − 1)f(y) for fixed k ∈ N\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any ap...

The aim of this paper is to introduce $n$-variables mappings which are cubic in each variable and to apply a fixed point theorem for the Hyers-Ulam stability of such mapping in non-Archimedean normed spaces. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes are presented.

This paper demonstrates methods for the online optimization of assistive robotic devices such as powered prostheses, orthoses and exoskeletons. Our algorithms estimate the value of a physiological objective in real-time (with a body "in-the-loop") and use this information to identify optimal device parameters. To handle sensor data that are noisy and dynamically delayed, we rely on a combinatio...

a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is crucial to obtain desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric inte...

3D InGaN/GaN microstructures grown by metal organic vapor phase epitaxy (MOVPE) and molecular beam epitaxy (MBE) have been extensively studied using a range of electron microscopy techniques. The growth of material by MBE has led to the growth of cubic GaN material. The changes in these crystal phases has been investigated by Electron Energy Loss Spectroscopy, where the variations in the fine s...