Studies on common fixed points By iteration methods

Abstract

The thesis deals mainly with common fixed point theorems and it consists newlineof five chapters newlineA history of metric space and various fixed point theories have been dis newlinecussed in the introductory chapter It also provides information about common newlinefixed point theorems and their origins and includes a brief survey on Banach s newlinecontraction principle newlinePointwise R weakly commuting and compatible are replaced into occasion newlineally weakly compatible mappings which generalize the results of Sanjay Kumar newlineand Renu Chugh 2002 Vectorial version of two new concepts reciprocal conti newlinenuity and pointwise R weakly commuting have been introduced Using this we newlinegeneralize the result of Sanjay Kumar and Renu Chugh 2002 newlineThere are various compatible type mappings in fixed point theory Two newlinenew concepts namely Cauchy compatible and Cauchy reciprocal continuous have newlinebeen introduced Cauchy compatible and Cauchy reciprocal continuous which newlinegeneralize compatible and reciprocal continuous respectively in the setting of newlinemetric spaces The main result generalizes many theorems newline newline