Research On Tripled Fixed Common Point Problems In Probabilistic Metric Spaces

In probabilistic metric spaces, the distance between two elements is measured by a distribution function and an ordinary metric space can be viewed as a special case of a probabilistic metric space. Consequently, the research of nonlinear operators in PM-spaces is of great significance. In this thesis, some nonlinear problems in PM-spaces are studied. It is divided into the following four sections.In chapter one, the backgrounds and current situation of operator theory in PM-spaces are introduced and the preliminaries of PM-spaces are given.In chapter two, introduce the concept of tripled common fixed point for a pair of mappings T:X×X×X→X,A:X→X in generalized Menger probabilistic metric spaces. Utilizing the properties of the pseudo-metric and the triangular norm, some tripled common fixed point problems of hybrid probabilistic contractions with a gauge function φ are studied.In chapter three, establish the notion of compatibility for a pair of mappings T:X×X×X→X and g:X→X in partially ordered probabilistic metric spaces. Under not necessary commutative conditions, some tripled coincidence and tripled common fixed point problems of compatible mappings satisfying a more general nonlinear contractive condition are studied.In chapter four, utilizing topological degree theory, some conditions under which the semi-closed 1-set contractive operators has an intrinsic value and has an intrinsic element are established. Our results generalize and extend some corresponding ones in previous literatures.