There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

Proceedings of the National Academy of Sciences

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

Some Results on Fixed Points

In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.

/pdf/a-fixed-point-theorem-for-set-valued-quasi-contractions-in-b-3bjccxea2g.pdf

A fixed point theorem for set-valued quasi- contractions in b-metric spaces

Partial Hausdorff metric and Nadlerʼs fixed point theorem on partial metric spaces

Common fixed points of generalized contractions on partial metric spaces and an application

In this paper, we prove some coupled fixed point theorems involving a (@j,@f)-weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces. These results are analogous to theorems of Van Luong and Xuan Thuan (2011) [10] on the class of ordered partial metric spaces. Also, an application is given to support our results.

Coupled fixed point results for ( ψ,φ )-weakly contractive condition in ordered partial metric spaces

https://www.tpbin.com/Uploads/Subjects/8f427cf7-d8f8-4f6b-8197-0a9e3e07264e.pdf

Hassen Aydi

Papers

A fixed point theorem for set-valued quasi- contractions in b-metric spaces

Partial Hausdorff metric and Nadlerʼs fixed point theorem on partial metric spaces

Common fixed points of generalized contractions on partial metric spaces and an application

Coupled fixed point results for ( ψ,φ )-weakly contractive condition in ordered partial metric spaces

Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces