Common fixed point theorems in symmetric spaces employing a new implicit function and common property (E.A). — Bulletin of the Belgian Mathematical Society — Simon Stevin | HighBeam Research

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Common fixed theorems in spaces employing new implicit and common (E.A).

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Banach contraction has been and generalized several ways include the article due Jungck [15]. paper due Jungck [15] inspired vigorous activity around since its Sessa [32] the tradition weakening the condition in common fixed theorems by the notion weak commutativity. the appearance this notion, authors introduced similar conditions weak commutativity as: R-weak compatible mappings, mappings of (A), type type (C), (P) and compatibility whose comparisons and are available Murthy [22].

In the of metric well as spaces, contrastive do not the existence fixed points the space compact (cf. or the condition is by a stronger condition. recent years, mappings have it possible prove results strict contractions compact metric The study common fixed of noncompatible is a of investigation the recent and still to be interesting aspect further investigation. this regard, results contained Pant [23] special mention author has the existence common fixed of an contraction when underlying space not essentially

Rhoades [30,31] out an comparative study contraction conditions he introduced contraction conditions also established equivalence of contraction conditions. recent years, [29] utilized functions instead contraction conditions prove common point theorems. functions are fruitful due their unifying besides admitting contraction conditions. and Ali also proved results on fixed points self mappings implicit function. this paper, define a class of function and the same prove our because of versatility of several known unknown contraction in one One of most striking of our function (to introduced in next section) in the of triangular in the of the of our in this and this why we to prove results in spaces instead metric spaces.

Let X a nonempty A symmetric is a real function on X X such

(a) d y) = if and if x y,

(b) d(x,y) d(y,x) [for x,y [member X.


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As by (X, we denote nonempty set equipped with symmetric d X and it a space. The (X, d) which limiting are defined the usual is also called an The idea E-spaces is to Frechet Menger. For details, one see [2,9,11,13,35].

recently, Aamri Moutawakil [1] the notion property (E.A) is a of compatible as well noncompatible mappings utilize the to prove common fixed theorems for contractions in spaces. In continuation, Imdad Ali [12] shown that property (E.A) the required of ranges involved mappings to a of mappings. recently, Liu al. [20] the notion common property which is fact an of property to two of mappings utilize the to prove fixed points strict contractions.

Definition 1.1.[1] pair (S, of self of a space (X, is said satisfy the (E.A) if exists a in X that

[MATHEMATICAL EXPRESSION REPRODUCIBLE IN

Remark 1.1. that a (S, T) self mappings a

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