Abstract
We introduced n-tupled coincidence point for a pair of maps T:Xn→X and A:X→X in Menger space. Utilizing the properties of the pseudometric and the triangular norm, we will establish n-tupled coincidence point theorems under weak compatibility as well as n-tupled fixed point theorems for hybrid probabilistic ψ-contractions with a gauge function. Our main results do not require the conditions of continuity and monotonicity of ψ. At the end of this paper, an example is given to support our main theorem.
Highlights
Introduction and PreliminariesProbabilistic metric space was introduced by Menger [1] in the year 1942 by generalizing metric spaces in which a distribution function was used instead of nonnegative real number as value of the metric. we present some basic concepts and results which will be used in this paper.Throughout this paper we will denote R as the set of real numbers, R+ as the nonnegative real numbers, and Z+ as the set of all positive integers.If ψ : R+ → R+ is a function such that ψ(0) = 0, ψ is called a gauge function
We present some basic concepts and results which will be used in this paper
Let (X, F, Δ) be a Menger PM-space such that Δ is a t-norm of H-type
Summary
We will introduce n-tupled coincidence point, n-tupled fixed point, commutativity, compatibility, and weak compatibility in Menger space for function of higher dimension. Utilizing the properties of the pseudometric and the triangular norm, we will establish n-tupled coincidence point results as well as n-tuple fixed point results using weak compatibility of mappings for hybrid probabilistic ψcontractions with a gauge function in Menger spaces. Using Lemma 5, we obtain that FAxm(1),Axq(1) > 1 − λ for all p > m ≥ N; that is, {Axm(1)} is a Cauchy sequence.
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