Journal of Mathematical Extension
Volume:12 Issue: 4, Autumn 2018

In this paper, we define a generalized $c$-distance in $tvs$-cone$b$-metric spaces and introduce some results about its properties.Then we prove some new fixed point and common fixed point results(with the underlying cone which is not normal). Respective resultsconcerning mappings without periodic points are also deduced. Someexamples are presented to validate our obtained results. Anapplication to system of Fredholm integral equations is presented.

The numerical range of a simple graph G, named F(G), is the numerical range of its adjacency matrix A(G). The main purpose of this paper was to approximate F(G). Then, using this approximation, bounds for the largest and the smallest eigenvalues of G were proposed. In fact, lower bounds for the largest eigenvalues of G were presented in terms of disjoint induced subgraphs of G and the numerical range of the square of A(G).

In this work, a new subclass of function, $G_\lambda(n, \mu, \lambda):n \in N_0, \mu \geq 1, \\0 \leq \lambda \leq 1$, was defined using the S\v{a}l\v{a}gean differential operator involving the modified sigmoid function and subordination principle. The initial coefficient bounds and the Fekete-Szego functional of this class were obtained.

In this paper, some new inequality for generalized convex functions are obtained. Some applications for some generalized special means are also given.

Image zooming is one of the important issues of image processing that maintains the quality and structure of image. Zooming an image necessitates placing the extra pixels in the image data. Moreover, adding the data to the image must be consistent with the texture in the image in order to prevent artificial blocks. In this study, the required pixels are estimated using barycentric rational interpolation. The proposed method is a non-linear one which can preserve the edges and reduces the blur and block artifacts on the zoomed image. Numerical results are presented using PSNR and SSIM fidelity measures and they are compared to some other methods. The average PSNR of the original image and image zooming was 33.08 which can prove that image zooming is very similar to the original image. The experimental results revealed that the proposed method had a better performance compared to other methods and could provide good image quality.

In this paper, we introduce new operators on fractional integration that we call (k; s; h)-Riemann-Liouville, (k; s)-Hadamard and (k; s; h)-Hadamard fractional integral operators. We provesome of their properties. Then, using our proposed approaches, we establish some applications oninequalities.

We introduce the notions of algebraic and arithmetic derivation. As an application, we use the combinatorial decomposition of an ideal to provide a constructive method to find the algebraic invariants, as the arithmetical rank, for a family of squarefree monomial ideals, the $k$--complete ideals $I_k^n,$ also known as squarefree Veronese ideals of degree $k$.

Iterative methods for optimization can be classified into two categories: line search methods and trust region methods. In this paper, we propose a modified regularized Newton method without line search for minimizing nonconvex functions whose Hessian matrix may be singular. The proposed method is proved to converge globally if the Gradient and Hessian of the objective function are Lipschitz continuous. Moreover, we report numerical results that show that the proposed algorithm is competitive with the existing methods.