Generalization of Banach Contraction Principle in Two Directions

Abstract

We showed that the generalized contraction mapping defined on a closed convex subset of a weakly Cauchy normed space has a unique fixed point. Moreover, the sequence of iterates of any element in the domain of the given mapping is converging strongly to the fixed point of such a mapping

A Study on Common Fixed Point of Joint A;B Generalized Cyclic ϕ−abc Weak Nonexpansive Mappings and Generalized Cyclic Bakr1 2020Abstract and Applied Analysis

“…Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc ; r contraction mappings. These results are extensions and generalizations of previous results reported in[10,11,17,19,20].…”

Some Generalized Fixed Point Theorems of Contraction Type Mappings in Quasi Metric Spaces

“…This paper adjusts conditions on new defined contraction type of mapping; namely {a, d, c, r}-ctype on quasi metric space, checked the validation of existence of unique fixed point of such type, gives a generalization of theorem (1) with these adjustments, shows that Corollary (1) extends some of the results given in (El-Shobaky et al, 2007;Gregus, 1980;Wong, 1975)…”

Coupled Fixed Point Theorems for Some Type of Contraction Mappings in b -Cone and b -Theta Cone Metric Spaces

“…In 2021, Sahar [16] generalized coupled fixed point result for some generalized contraction type of mappings of Bhaskar and Lakshmikantham [12] and of Sahar [17,18] in theta cone metric spaces.…”