Abstract
In this paper, by using the known class Ψ∗ of 5-dimensional functions determined by the known classes {C ,Φu}, we discuss the existence problems of coincidence points for three mappings of integral type with semiimplicit contraction conditions and obtain a common fixed point theorem for two mappings on ordered metric spaces. Finally, we give a sufficient condition under which there exists a unique common fixed point.
Highlights
Introduction and preliminariesThroughout this paper, we assume that R+ = [0, +∞) andΦ = {φ : φ : R+ → R+| φ is Lebesgue integral, summable on each compact subset ofR+ and ε 0 φ (t)dt > for each ε > 0}The famous Banach’s contraction principle is as follows: YONGJIE PIAOTheorem 1.1([1]) Let f be a self mapping on a complete metric space (X, d) satisfying d( f x, f y) ≤ cd(x, y), ∀ x, y ∈ X, (1.1)where c ∈ [0, 1) is a constant
By using the known class Ψ∗ of 5-dimensional functions determined by the known classes {C, Φu}, we discuss the existence problems of coincidence points for three mappings of integral type with semiimplicit contraction conditions and obtain a common fixed point theorem for two mappings on ordered metric spaces
Ansari and Piao et al[18] discussed and obtained several common fixed point theorems for two mappings of integral type with semi-implicit contractive conditions determined by functions F ∈ C and φ ∈ Φu and ψ ∈ Ψ∗ in metric spaces
Summary
Definition 1.2([18]) Let Φu be a set of all functions φ : R+ → R+ satisfying the following conditions: (i) φ is continuous; (ii) φ(t) > 0 for all t > 0 and φ(0) ≥ 0.
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