Fixed Point Theorems for Contractive Type Mappings in Distance Spaces

Abstract

Weoftencomeacrossnonlinearsystemsandtheirassociatednonlinearequa- tionsandbothpureandappliedmathematicsplayavitalroleindealing with suchkindofequations. When wetalkaboutnonlinearanalysis,itsfundamentalimportancein physical,biological,engineeringandtechnologicalsciencescanbeseenin the formulationandanalysisofvariousclassesofequation. As faras xedpointtheoryisconcerned,itsextensivenesscanbeseenby its applicationsinvarious elds.Theoremsthatareconcernedwiththeex- istenceandpropertiesof xedpointsareknownas xedpointtheorems. Thesetheoremsplayaveryimportantroleforprovingtheexistenceand uniquenessofsolutionsforvariousmathematicalmodels.Metric xedpoint theoryhastakenonnewdimensionssincetheinceptionofthewellknown Banachcontractionprinciple,andthiscontractionprinciplegivesusareally suitablebaseto nd xedpointforselfmappings.Themainaimofthis thesisistoaddsomemorewidelyapplicableresultstotheliterature.