We study how the fixed point subgroup of an automorphism influences the structure of a group.

In this paper, we obtain several new continuous selection theorems for multi-valued mappings on completely regular spaces and fixed point theorems for multi-valued maps on nonmetrizable spaces. They, in particular, provide a partial solution of a conjecture of X. Wu.

In this investigation, our aim is to develop the definition of mild solutions for impulsive fractional differential equations of order α ∈ (1,2) and obtain some sufficient conditions for existence of mild solutions using the analytic operator functions and fixed point theorems. We also verify the existence result with an example involving partial derivative.

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture, the Arnold fixed point conjecture.

In this article, we study the notion of virtually repelling fixed point. We first give a definition and an interpretation of it. We then prove that most proper holomorphic mappings f : U → V with U contained in V have at least one virtually repelling fixed point. 1. Preliminaries Let f : (C, α) → (C, α) be a holomorphic germ fixing α. Definition 1. The multiplicity m of α as a fixed point of f ...

We prove two general theorems, which appear to be very useful in investigation of the Hyers-Ulam stability of a higher order linear functional equation in single variable, with constant coefficients. We give several examples of their applications. In particular we show that we obtain in this way several fixed point results for a particular operator. The main tool in the proofs is a complexifica...

We give an explicit construction of sharply 2-transitive groups with fixed point free involutions and without nontrivial abelian normal subgroup.

In this paper, we prove some common fixed point theorems for two pairs of weakly compatible selfmaps satisfying a new ψ-contractive condition in the framework of a partial metric space. We also provide illustrative examples in support of our new results. The results obtained in this paper differ from the recent relative results in literature. c ©2016 All rights reserved.

The purpose of this paper is to obtain some coincidence and fixed point theorems for a generalized hybrid pair of single-valued and set-valued non continuous maps. Our results generalize some recent results.

The aim of this paper is to establish some common fixed point theorems under occasionally weakly compatible maps using implicit functions.