Coincidence Point Theorems In F-type Topological Spaces

In this dissertation, we apply a pseudo-ordering principle given by Bae et al. [J. Korean Math. Sco. 31(1)(1994) 29-48] to study the coincidence point theory in F-type topological spaces. The main contents are as follows:(1) In chapter 1, as preliminaries, we recommend the definition of F-type topological space and its characterization, several examples of such spaces are presented. And then, we introduce the Bae-Cho-Yeom pseudo-ordering principle and the related results.(2) In chapter 2, we first introduce a reflexive relation (?) on F-type topological spaces and define the concepts of (?)-increasing sequence, <-nondecreasing ((?)-nonincreasing) function and (?)-lower semi-continuous function etc by using it. On the baises of this, by using the Bae-Cho-Yeom pseudo-ordering principle, we establish some new coincidence point theorems for single-valued and set-valued mappings in F-type topological spaces, and give several important corollaries.(3) In chapter 3, as a direct application of the main results in chapter 2, we get several corresponding coincidence point theorems for single-valued and set-valued mappings in complete fuzzy metric spaces.(4) In chapter 4, as another direct application of the main results in chapter 2, we give some coincidence point theorems for single-valued and set-valued mappings in complete Menger probabilistic metric spaces.The main results presented in this paper, which unify and generalize the Caristi fixed point theorem [5], the Downing-Kirk fixed point theorem [12], the Bae-Cho-Yeom fixed point theorem, the coincidence point theorems of Chang et al. [8], Jung et al [17, 18], and the corresponding results in [2,4,6,7,15,16,24,25].