Studies on fixed point theorems and best proximity point theorems

Abstract

In this thesis, we provided few fixed point theorems and best prox- newlineimity point theorems for certain class of mappings, which generalize newlinesome well-known theorems in the literature. newlineIn chapter 1, we provide a brief literature survey on fixed point newlinetheorems and best proximity point theorems. newlineIn chapter 2, we consider an asymptotically nonexpansive type newlinemappings and provide the sufficient conditions for the existence of newlinefixed points of such class of mappings. newlineIn Chapter 3, we consider an upper semicontinuous multivalued newlinenonself mappings for which the sequence of iteration is meaningless. newlineHence we introduce new type of iteration called generalized Picard newlineiteration-like sequence and used to prove the existence of best prox- newlineimity points of upper semicontinuous multivalued nonself mappings. newlineAs an application, we obtained sufficient conditions for the existence newlineof a best proximity points for multivalued contractive mappings. newlineIn Chapter 4, we introduced a new class of mappings called cyclic newlinep-continuous mappings which need not have best proximity points. So newlinewe provide a characterization for the existence of best proximity point newlinefor such type of mappings. newlineIn Chapter 5, we consider a nonself nonexpansive mapping T : A ! newlineB, where A,B are nonempty subsets of a real Hilbert space H. We newlineprovide an algorithm to approximate a best proximity point of T. newline