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...

In this paper, we establish the existence and stability results for (?k,?k)-Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point integral boundary conditions. We achieve formulation of solution to differential equation constant coefficients in term Mittag–Leffler kernel. The uniqueness result is proved by applying Banach’s fixed point theory pr...

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

The Hyers–Ulam stability of the conditional quadratic functional equation of Pexider type f(x + y) + f(x − y) = 2g(x) + 2h(y), x ⊥ y is established where ⊥ is a symmetric orthogonality in the sense of Rätz and f is odd. ∗2000 Mathematics Subject Classification. Primary 39B52, secondary 39B82.

The generalized Hyers-Ulam-Rassias stability proposition in respect of the quadratic functional equation namely f(x+y+z)+f(x−y)+f(x−z) = f(x−y−z)+f(x+y)+f(x+z) is what is taken into account to be dealt with in this paper.

In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n, H n (A, X) = 0 if and only if the n-th cohomology group approximately vanishes.