Journal of Mathematical Extension
Volume:10 Issue: 1, Winter 2016

We will introduce a new class of implicit functions to prove a common fixed point theorem for multi-valued mappings in ultrametric spaces. Our result enable us to give a genuine generalization of  some known fixed point theorems, provided that the underling space is ultrametric.

In this paper, we define an H(·, ·)-mixed relaxed co-ηmonotone mapping and we apply the same for solving a resolvent equation problem in Hilbert spaces. We also prove some of the properties of H(·, ·)-mixed relaxed co-η-monotone mapping. A mann-type iterative algorithm is developed to approximate the solution of resolvent equation problem. Convergence of the iterative sequences is also demonstrated. In support of the concept of H(·, ·)-mixed relaxed co-η-monotone mapping, we construct an example.

In this paper, we construct all classes of 3×3 strongly clean upper triangular matrices over Z. Moreover, necessary and sufficient conditions under which a 3×3 upper triangular matrix over Z is strongly clean are given.

Using the fixed point method, we establish the stability of $m-$Lie homomorphisms and Jordan $m-$Lie homomorphisms on $m-$Lie algebras  associated to the  followingadditive functional equation $$2\mu f\left(\sum_{i=1}^m  m x_i\right)=\sum_{i=1}^mf\left(\mu  \left(m x_i + \sum_{j=1~,i\neq j}^m x_j\right)\right)+f\left(\sum_{i=1}^m \mu x_i\right)$$where $m$ be an integer greater than 2 and all $\mu\in  \Bbb T_{\frac{1}{n_0}} :=\left\{e^{i\theta} \ ;\0\leq\theta\leq \frac{2\pi}{n_0}\right\}$.

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The purpose of this paper is to present some new couple fixed point theorems for multivalued mappings which satisfy generalized weak contraction in ordered metric spaces. The results of this paper are generalizations of the main results of [3, 5, 9]. As an application, we show existence and uniqueness of solutions of a class of nonlinear integral equations.

A lot of methods and models in classical reliability theory assume that all parameters of lifetime density function are precise. But in the real world applications imprecise information is often mixed up in the lifetimes and/or parameters of systems. However, the parameters sometimes cannot be recorded precisely due to machine errors, experiment, personal judgment, estimation or some other unexpected situations. When parameters in the lifetime distribution are intervalvalued, the conventional reliability system may have difficulty for handling reliability function. Therefore, estimation methods for reliability characteristics have to be adapted to the situation of interval-valued parameters of life times in order to obtain more realistic results. In this regard, the present paper will discuss the system reliability for coherent system based on a new notion of random variable with interval-valued parameters. The concepts of probability density function and cumulative distribution function of the random variable with interval-valued parameters will be stated in this paper. Using the same techniques in classical probability theory, the probability measure of the random variable can be constructed from the probability density function and cumulative distribution function. In the proceeding discussion, several numerical examples are provided in reliability systems and queueing theory to clarify our discussions.

In this paper, we consider the integral equation of convolution type with some conditions which has two kernels. At first we change this integral equation to a simple operator form and then, we approximate it by Topelitzian and Hankelian series.

In this article, we will propose a new approach for evaluating congestion in decision making units (DMUs) by weight restriction using common weights based on comparison of inputs. The main advantage of the proposed method is to solve one linear programming for all DMUs. Therefore, this method greatly reduces the computational costs. The proposed model for measuring congestion will be shown by examples.