‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

It is known that the variational inequality problem (VIP) can be converted to a differentiable unconstrained optimization problem via a merit function first considered by Peng and later studied further by Yamashita, Taji and Fukushima. This merit function, called the D-gap function, though is differentiable, is not twice differentiable and its generalized Hessian with existing definitions is ve...

If the world is a differential equation, as Boltzmann thought, the problem of the origin of the "nowhere differentiable nature of reality" (cf. Mandelbrot [1]) poses itself [2]. To our knowledge, only two differentiable maps exist in the literature which produce nowhere differentiable behavior, the 3-D diffeomorphisms indicated by Grebogi et al. [3] and by Kaneko [4], The first map [3] which co...

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....