Fixed points for G-contractions on uniform spaces endowed with a graph

Abstract

In this paper, we generalize some main results of (Jachymski in Proc. Am. Math. Soc. 136:1359Soc. 136: -1373Soc. 136: , 2008) from metric to uniform spaces endowed with an E -distance and a graph using a new type of contractions by employing a class of nondecreasing functions. MSC: 47H10; 05C40

Fixed points for Kannan type contractions in uniform spaces endowed with a graph

“…for if k, a and b are any arbitrary positive numbers satisfying k < 1 and a < b, then putting x = 1 and y = 3 5 yields…”

“…In 2008 Jachymski [6] established Banach fixed point theorem in metric spaces with a graph and his idea followed by the authors in uniform spaces (see, e.g., [2,3]).…”

Fixed points of integral type contractions in uniform spaces

“…We begin with some basics in uniform spaces which are needed in this paper. The reader can find an in-depth discussion in, e.g., [7] and recent results on the fixed points in uniform spaces in [3].…”

An Order Theoretic Approach to the Banach Contraction Principle in Modular Spaces

“…Without loss of generality, we may suppose that ck < 1 2 . Otherwise, choose the integer n such that c n k < 1 2 and then replace T n by T . Let x ∈ X ρ ; we show that {T n x} is a ρ-Cauchy sequence.…”

“…The approach given in the proof of Theorem 3 may also be seen in [4]. The idea given in the remark above is, in fact, a simple use of uniform space techniques in fixed point theory (see e.g., [1,2]).…”