Abstract
The aim of this paper is to obtain some new important consequences related to coupled coincidence points via C-class functions in the context of a regular partial ordered complete b-metric-like space (for short, RPOCbML space); this space arises from combining the results of b-metric-like space with partial metric space and adding the regularity condition. Finally, we support our theoretical results by some examples and an application about finding an analytical solution for nonlinear integral equations.
Highlights
Introduction and elementary discussions Fixed point theory is one of the most important branches of non-linear analysis because it contributes to many disciplines such as economics, engineering and game theory, mathematics, and others
In 1992, Matthews [2] circulated the principle of Banach to partial metric space as follows: Definition 1
We present some examples and an application to find the existence of solution of nonlinear integral equation to support our work
Summary
Theorem 1 Let (Υ, , ωb) be a RPOCbML space (with a coefficient s > 1). Assume that , : Υ × Υ → Υ are two mappings such that the following conditions are satisfied:. Since ηn = max ωb( (an, cn), (an+1, cn+1)), ωb( (cn, an), (cn+1, an+1)) , both sequences { (an, cn)} and { (cn, an)} are Cauchy in the complete space (Υ, ωb), and since (Υ × Υ) ⊆ (Υ × Υ) and (Υ × Υ) is closed, there exist a, c ∈ Υ such that lim n→∞. By the regularity of the space (Υ, ωb, ), we get (an, cn) (a, c) and (cn, an) (c, a) It follows from (1) that ψ(sαωb( (an, cn), (a, c))) ≤ f (ψ (max{ωb( (an, cn), (a, c)), ωb( (cn, an), (c, a))}) ,. Theorem 2 In addition to the hypotheses of Theorem 1, suppose that for every (a, c), (a∗, c∗) in Υ × Υ , there exists another (l, m) in Υ × Υ which is comparable to (a, c) and (a∗, c∗), and have a unique coupled coincidence point.
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