Aiman Mukheimer

Some common fixed point theorems in complex valued b-metric spaces.

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valued b-metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self-mappings on complex valued b-metric spaces. Some examples are given to illustrate the main results.

Banach contraction principle for cyclical mappings on partial metric spaces

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.MSC:47H10, 54H25.

Some Common Fixed Point Theorems in Complex Valuedb-Metric Spaces

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valued b-metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self-mappings on complex valued b-metric spaces. Some examples are given to illustrate the main results.

Pointwise convergence of wavelet expansions associated with dilation matrix

The wavelet expansion associated with dilation matrix of a function is studied. This expansion is shown to converge uniformly on compact subsets

Modified Lagrangian Methods for Separable Optimization Problems

We propose a convergence analysis of a new decomposition method to solve structured optimization problems. The proposed scheme is based on a class of modified Lagrangians combined with the allocation of resources decomposition algorithm. Under mild assumptions, we show that the method generates convergent primal-dual sequences.

Convergence of a Proximal Point Algorithm for Solving Minimization Problems

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Guler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones.

Wardowski Type Contractions and the Fixed-Circle Problem on -Metric Spaces

In this paper, we present new fixed-circle theorems for self-mappings on an -metric space using some Wardowski type contractions, -contractive, and weakly -contractive self-mappings. The common property in all of the obtained theorems for Wardowski type contractions is that the self-mapping fixes both the circle and the disc with the center and the radius .

Some Common Fixed Point Theorems in Complex Valued -Metric Spaces

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valued b-metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self-mappings on complex valued b-metric spaces. Some examples are given to illustrate the main results.

On two-dimensional whooping cough dynamics of diffusion type

This article analyses two-dimensional whooping cough model with diffusion term. The resulting two coupled partial differential equations are solved numerically by employing homotopy analysis method HAM. Convergence of the derived iterative schemes is highlighted and illustrative examples have been presented. It is noticed that the numerical and graphical results are consistent with the dynamical behaviour of the disease.