Analysis Laboratory

Mathematical analysis (analysis for short) is a broad field of mathematics that has evolved from calculus and the theory of real and complex functions. Analysis is the study of spaces and functions which have the notion of “nearness” and “distance” which allows limiting processes to be studied. Analysis maintains connections with multiple diverse topics in science and technology. 

Our group pursues several paths of investigation in analysis to improve understanding of the subject and to develop mathematical results that lay the groundwork for applications. In our group we are mainly working in : functional analysis and its applications, such as function and sequence spaces, modular and Orlicz spaces, Banach lattice, ordered convergence, and optimization; operator theory; measure and integral theory; fixed point theory; topology; differential equations; quantitative description related to real functions; Baire class one functions; domain theory.

Some of the current research topics in our group include :

  • various kinds of the Stieltjes integral mainly using the gauge integration; 
  • topological properties and functions defined by means of neighbourhood assignments;
  • the study of Banach-Saks properties from order convergence point of view;
  • ordinal indices of real functions and sequence of real functions;
  • some relation between generalized metric spaces and some concepts in domain theory;
  • the characteristics of the solutions to the ergodic problem resulting in the study of homogenization of Hamilton-Jacobi equations in the viscosity sense.