Some fixed point theorems in Menger spaces and applications

Fixed Point Theory is a beautiful mixture of analysis (pure and applied), topology and geometry. Fixed point theorems give the conditions under which mappings (single or multivalued) have solutions. The fixed point theory in probabilistic metric spaces is useful in the study of existence of solutions of operator equations in probabilistic metric space and probabilistic functional analysis, which is a very dynamic area of mathematical research. The notion of a probabilistic metric space corresponds to the situations when we do not know exactly the distance between two points; we know only probabilities of possible values of this distance. This book contains six chapters. New fixed point theorems for contraction mappings, expansion mappings, probabilistic densifying mappings are obtained in Menger spaces. Also related fixed point theorems in Menger spaces and applications of fixed point theorems are studied. This book will help the researchers studying fixed point theory.