Fixed points theory and non-linear analysis

MAM intensive research course for PhD students and researchers.
MAM research frontier lecture series.

Topics:

1) Fixed Point Theory and its Applications,

2) Some extensions of nonlinear ergodic theorem,

3) Iterated Function Systems and the Global Construction of Fractals

 

October 9 and October 10, 2019

Wednesday October 9, 13.15-15.00,

U3-083 (Hilbert room), Mälardalen university, Västerås:

Title: Fixed Point Theory and its Applications

Dr. Talat Nazir, Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan

Abstract: In a wide range of mathematical problems the existence of a solution is equivalent to the existence of a fixed point for a suitable map. The existence of a fixed point is therefore of paramount importance in several areas of mathematics and other sciences. Fixed point results provide conditions under which maps have solutions. The theory itself is a beautiful mixture of analysis (pure and applied), topology, and geometry.

Over the last 50 years or so the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory, and physics.

In this talk, we present several fixed point results for mappings that are satisfying certain types of general contractive conditions in the setup of generalized metrics spaces. Periodic point results and stability of these results are also presented. Common fixed point results of mappings are obtained under the weaker commuting conditions. Some applications of these results will also establish.

 

Wednesday October 9, 15.15-17.00:

U3-083 (Hilbert room), Mälardalen university, Västerås:

Title: Some extensions of nonlinear ergodic theorem

Professor Mujahid Abbas, Department of Mathematics, Government College University, Lahore, Pakistan

Abstract (pdf 45 kB)

 

Thursday October 10, 13.15-17.00:

U3-083 (Hilbert room), Mälardalen university, Västerås:

Title: Iterated Function Systems and the Global Construction of Fractals

Dr. Talat Nazir, Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan

Abstract:

Iterated function systems are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry.
In this talk, we construct the fractals with the help of finite family of generalized contractive operators in the setup of distance spaces. Varieties of results for generalized iterated function system are established that converges to the attractors of Hutchinson operators. The stability of these results is also established. Applications and examples are also obtained from main results presented therein.