A New Class of Linear Rational Contractions in Fuzzy Metric Spaces
Makhan Satpute *
Department of Mathematics, Govt. Narmada PG College, Narmadapuram (M.P.), PIN – 461001, India and Department of Mathematics, Institute for Excellence in Higher Education, Bhopal, M.P., India.
Manoj Ughade
Department of Mathematics, Mahatma Gandhi Govt. P. G. College, Itarsi, M.P., India.
Rashmi Tiwari
Department of Mathematics, Govt. Narmada PG College, Narmadapuram (M.P.), PIN – 461001, India.
Kamal Vadhawa
Department of Mathematics, Govt. Narmada PG College, Narmadapuram (M.P.), PIN – 461001, India.
*Author to whom correspondence should be addressed.
Abstract
We introduce and investigate a new class of contractive mappings on fuzzy metric spaces, called linear rational contractions. These mappings combine linear and rational contractive properties and extend known contraction principles in fuzzy settings. Existence and uniqueness of fixed points are established under mild assumptions. We further present several fixed point theorems for generalized classes of linear rational contractions, obtain convergence results, and provide illustrative examples. The results unify and extend various classical fixed point principles in the framework of fuzzy metric spaces.
Keywords: Fuzzy metric space, linear rational contraction, fixed point theorems, banach-type contraction, cyclic mapping