Weak forms of open mappings and α -topology

Some Weaker Forms of Fuzzy Faintly Open Mappings

This paper is devoted to introduce and investigate some weak forms of fuzzy open mappings, namely fuzzy faintly semi open (fuzzy faintly semi closed), fuzzy faintly preopen (fuzzy faintly preclosed), fuzzy faintly α-open (fuzzy faintly α-closed), fuzzy faintly semi preopen (fuzzy faintly semi preclosed) and fuzzy faintly spopen (fuzzy faintly spclosed) mappings and their fundamental properties ...

Expansion of α-open sets and decomposition of α-continuous mappings

In 1965, Njastad [2] introduced the notion of α-sets in topological space. In 1983, Mashhour et al. [1] introduced, with the help of α-sets, a weak form of continuity which they termed as α-continuity. Noiri [3] introduced the same concept, but under the name strong semicontinuity. Noiri [4] defined with the aid of α-sets a new weakened form of continuous mapping called weakly α-continuous mapp...

Topology Proceedings 8 (1983) pp. 195-212: WEAK CONFLUENCE AND MAPPINGS TO ONE-DIMENSIONAL POLYHEDRA

Weak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...

Modular Forms and Topology

We want to discuss various applications of modular forms in topology. The starting point is elliptic genus and its generalizations. The main techniques are the Atiyah-Singer index theorem, the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, Kac-Moody Lie algebras, modular forms and theta-functions. Just as the representations theory of classical Lie groups has close connections with the...