By considering scalar theories on the fuzzy sphere as matrix models, we construct a renormalization scheme and calculate the one-loop effective action. Because of UVIR mixing, the twoand the four-point correlators at low energy are not slowly varying functions of external momenta. Interestingly, we also find that field theories on fuzzy RP2 avoid UV-IR mixing and hence are much more like conven...

The fixed point alternative methods are implemented to giveHyers-Ulam  stability for  the quintic functional equation $ f(x+3y)- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and thesextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$   in the setting ofintuitionistic fuzzy normed spaces (IFN-spaces).  This methodintroduces a met...

This paper gives three noncompact variants of Lefschetz–Nielsen fixed-point theory parallel to developments that have occurred in surgery theory. Thus, we study when a proper map can be properly homotoped, or boundedly homotoped, or even homotoped in a C bounded fashion to a fixedpoint free map. As an example, the universal cover of a compact aspherical manifold always has a fixed-point free se...

This chapter presents a summary of recent results obtained in game and social choice theories, and highlights the application and the development of tools in algebraic topology . The purpose is expository : no attempt is made to provide complete proofs, for which references are given, nor to review the previous work in this area, which covers a significant subset of the economic literature . Th...

We call proof mining the process of logically analyzing proofs in mathematics with the aim of obtaining new information. In this survey paper we discuss, by means of examples from mathematics, some of the main techniques used in proof mining. We show that those techniques not only apply to proofs based on classical logic, but also to proofs which involve non-effective principles such as the att...

We establish common fixed point theorems for weakly compatible generalized φcontractions. As applications, various common fixed point and best approximation results for Cq-commuting and compatible maps are derived. Our results unify, extend and complement various known results existing in the literature.

A fixed point theorem for condensing maps due to Martelli combined with theories of a strongly continuous cosine family of bounded linear operators is used to investigate the existence of solutions to second order impulsive neutral functional integrodifferential inclusions with infinite delay in Banach spaces.

We show that under some assumptions on the function f the system ż = z(f(z)e + ei2φt) generates chaotic dynamics for sufficiently small parameter φ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.