Theory of Approximation and Applications
Volume:11 Issue: 2, Summer and Autumn 2017

This paper is concerned with a technique for solving Fredholm integro-di erential equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained. The analytical solution is represented in the form of series. An iterative method is given to obtain the approximate solution. The convergence analysis is established theoretically. The applicability of the iterative method is demonstrated by testing some various examples.

We suggest a explicit viscosity iterative algorithm for nding a common element of the set of common xed points for W-mappings which solves some variational inequality. Also, we prove a strong convergence theorem with some control conditions. Finally, we apply our results to solve the equilibrium problems. Finally, examples and numerical results are also given.

Recently Abbasbandy and Hajjari (Computers and Mathematics with Applications 57 (2009) 413-419) have introduced a ranking method for the trapezoidal fuzzy numbers. This paper extends theirs method to all fuzzy numbers, which uses from a defuzzi cation of fuzzy numbers and a general weighting function. Extended method is interesting for ranking all fuzzy numbers, and it can be applied for solving and optimizing engineering and economics problems in a fuzzy environment.

In many applied programs in real-life problems, both physical inputs and outputs are heterogeneous which in this case the ecient cost and income model can not apply to evaluate the cost and income of related turnover. So, a measurement based on the directional value of pro t was presented which we have developed it in this paper and have computed it for interval data. In fact, we have measured the ineciency of cost in presence of interval data using the directional distance function which is mostly meaningful for those companies that their essential behavioral goals are maximizing the pro t with least ambiguity. To this end, considering some branches of Tejarat bank in Iran, the eciency of pro t in presence of interval data is computed by means of the distance directional function.

This paper we investigate the existence and uniqueness of solutions to fuzzy di erential equations driven by Liu's process. For this, it is necessary to provide and prove a new existence and uniqueness theorem for fuzzy di erential equations under weak Lipschitz condition. Then the results allows us to consider and analyze solutions to a wide range of nonlinear fuzzy di erential equations driven by Liu's process.

In this letter, we established a traveling wave solution by using cosine function algorithm for Gardner equation and (2)-dimensional breaking soliton system. The cosine method is used to obtain the exact solution.

Fuzzy integral equations have a major role in the mathematics and applications. In this paper, general fuzzy integral equations with nonlinear fuzzy kernels are introduced. The existence and uniqueness of their solutions are approved and an upper bound for them are determined. Finally an algorithm is drawn to show theorems better.