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We prove the generalized Hyers–Ulam stability of the Cauchy functional equation f (x + y) = f (x) + f (y) and the quadratic functional equation f (x + y) + f (x − y) = 2f (x) + 2f (y) in non-Archimedean normed spaces.

In this paper, we develop a new cubic spline method for computing approximate solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and gives approximations which are better than those produced by some other collocation, finite difference… (More)

- Chun-Gil Park, Themistocles M Rassias, K Ciesielski
- 2008

In this paper, we prove the generalized Hyers–Ulam stability of the isometric additive mappings in generalized quasi-Banach spaces, and prove the generalized Hyers–Ulam stability of the isometric additive mappings in generalized p-Banach spaces.

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation with nonlocal conditions. The results are obtained by using the Leray-Schauder alternative fixed point theorem. An example is provided to illustrate the theory.

According to semigroup theories and Sadovskii fixed point theorem , this paper is mainly concerned with the existence of solutions for an impulsive neutral differential and integrodifferential systems with nonlocal conditions in Banach spaces. As an application of this main theorem, a practical consequence is derived for the sub-linear growth case. In the… (More)

- VASILE CIRTOAJE, Themistocles M. Rassias
- 2011

The main aim of this paper is to give a complete proof to the open inequality with power-exponential functions a ea + b eb ≥ a eb + b ea , which holds for all positive real numbers a and b. Notice that this inequality was proved in [1] for only a ≥ b ≥ 1 e and 1 e ≥ a ≥ b. In addition, other two open inequalities with power-exponential functions are proved,… (More)