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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)
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  for only a ≥ b ≥ 1 e and 1 e ≥ a ≥ b. In addition, other two open inequalities with power-exponential functions are proved,… (More)
In this paper, we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the Wiener–Hopf equations technique. The modified methods converge for pseudomonotone operators. Our proof of convergence is very simple as compared with other methods. The proposed methods include several known methods… (More)
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)