Some problems of fixed point theorems in different spaces.

      Аннотация: The book comprises of seven chapters. In chapter -I, we have given a brief history of Fixed Point Theory and its applcation. In chapter -II, we have introduced the concept of tripled best proximity point in metric spaces. As an application to our main result, we prove some tripled best proximity point theorems in metric spaces. In chapter -III, we have developed tripled coincidence point theorems in ordered cone metric spaces over a solid cone. Chapter -IV is divided into three sections: In All section has deal with the results of Fuzzy metric spaces to establish common coincidence point. In chapter -V, we have proved some periodic point and fixed point theorems for a rational inequality in complex valued metric spaces. Also, we have given an application for our main theorem in complex valued metric spaces. In chapter -VI, we focus on various tools of obtaining Fixed Point such as various kinds of compatible maps (for example: Compatible Maps of Type(A), Type(B), Type(C), Type(P), weakly compatible maps, etc.) for details of tools in Fixed Point Theorems we refer Murthy([124]). We have shown that these pairs satisfy a contractive condition.

Ключевые слова: fixed point, best proximity, point functional analysis