Fixed Point Theory, Ulam stability and related applications


Janusz Brzdek, Pedagogical University,  Krakow, Poland.

E-Mail: jbrzdek@up.krakow.pl

Erdal Karapınar, Atılım University, Ankara, Turkey.

E-Mail: erdal.karapinar@atilim.edu.tr



            Due to its possible applications, Fixed Point Theory in metric spaces has a key role in Nonlinear Analysis. In the last fifty years, discussing the existence and uniqueness of fixed points of single and multivalued operators in different kind of spaces (such as quasimetric spaces, pseudo-quasi-metric spaces, partial metric spaces, b-metric spaces and fuzzy metric spaces, among others) has attracted the attention of several researchers in the field of Nonlinear Analysis. The enormous potential of its applications to almost all quantitative sciences (such as Mathematics, Engineering, Chemistry, Biology, Economics, Computer Science, and other sciences) justify the great interest in this area.

            The purpose of this workshop is to bring together Mathematicians, and also all researchers which might be interested in this topic, a forum to present, to share and to discuss their main advances in this area (ideas, techniques, possible results, proofs, etc.)

            Topics in this special session include, but are not limited to:

  • Fixed Point theory in various abstract spaces
  • Existence and uniqueness of coupled/tripled/quadrupled fixed point
  • Coincidence point theory
  • Existence and uniqueness of common fixed points
  • Well-posedness of fixed point results
  • Advances on multivalued fixed point theorems
  • Fixed point methods for the equilibrium problems and applications
  • Iterative methods for the fixed points of the nonexpansive-type mappings
  • Picard operators on various abstract spaces
  • Applications to different areas
  • Stability of difference, differential, functional, and integral equations
  • Stability of inequalities and other mathematical objects
  • Hyperstability and superstability
  • Various (direct, fixed point, invariant mean, etc.) methods for proving Ulam’s type stability results
  • Generalized (in the sense of Aoki and Rassias, Bourgin and Găvruţa) stability
  • Stability on restricted domains and in various (metric, Banach, non-Archimedean, fuzzy, quasi-Banach, etc.) spaces
  • Relations between Ulam’s type stability and fixed point results