A Study on Multidimensional Fixed Point Results on Various METRIC SPACES WITH APPLICATIONS

Abstract

vi newlineABSTRACT newlineIn this thesis we studied some coupled fixed points and quadruple fixed points newlinevia Suzuki contractive type, C class function contractive type, generalized Banach newlinecontractive type and integral contractive type conditions in Ab metric spaces, newlineSb metric spaces, G metric spaces and bipolar metric spaces respectively. In this newlineconnection we also provided applications to integral equations as well as homotopy, newlinealso we gave some suitable examples to support our main results in each Chapters. newlineWe divided our total work into 5 Chapters. newlineIn Chapter 1, we mentioned definitions, examples, lemmas, previous results newlineand notations which are going to brief survey of literature as well as basics of our newlineremaining Chapters. newlineIn Chapter 2, we obtained unique common coupled fixed point theorems in newlinecomplete Ab metric spaces by using Suzuki type generalized contractive conditions. We provided applications to integral equations as well as homotopy. We newlinealso furnished some corollaries and examples to support our main result. newlineThis work is published in International Journal of Analysis and Applications, newlineVol. 20:67, PP. 1-18, (2022) (Scopus Indexed and Web of Science). newlinehttps://doi.org/10.28924/2291-8639-20-2022-67. newlineIn Chapter 3, we obtained unique common coupled fixed point theorems via newlineC class functions in complete Sb metric spaces. We gave applications to integral newlineequations as well as homotopy. We also mentioned some corollaries and examples newlineto support our results. newlineThis work is published in International Journal of Nonlinear Analysis and Applications, PP. 1-17, (2023) (Scopus Indexed). newlinehttp://dx.doi.org/10.22075/ijnaa.2023.29959.4302. newlineIn Chapter 4, we obtained unique common coupled fixed point theorems by newlineusing generalized Banach contraction conditions which involve altering distance newlinevii newlinefunction in complete G metric spaces along with applications to integral equations newlineas well as homotopy. We discussed some corollaries and examples to support our newlineresults. newlineThis work is published in Communications in Mathematics and Applications, newlineVol