Abstract
In this manuscript, using CLR property, coupled coincidence and common coupled fixed point results for two-hybrid pairs satisfying (F,φ)- contraction are demonstrated. Using the established results existence of solution to the coupled system of functional and nonlinear matrix equations is also discussed. We provide examples where the main theorem is applicable but most current relevant results in literature fail to have a common coupled fixed point.
Highlights
Introduction and PreliminariesThe existence and uniqueness of solution of a nonlinear matrix equations and functional equations are very interesting research area
Matrix equations and functional equations often arise from various areas, such as ladder networks [7, 8], control theory [9, 10], and dynamic programming [11,12,13,14]
Banach [15] has sorted out successful and well-known result; such consequence was later on named as Banach contraction principle (BCP)
Summary
The existence and uniqueness of solution of a nonlinear matrix equations and functional equations are very interesting research area. Imdad et al [24] defined common limit range property for a hybrid pair of mappings and demonstrated fixed point results in the symmetric (semimetric) spaces. Motivated by the above results, we studied common coupled fixed point results by defining the concept of CLR property for two hybrid pairs of mapping via generalized (F, φ) type contraction. G : Θ → Θ and S, T : Θ → CB(Θ) defined on a metric space (Θ, d), are to satisfy the common limit in the range of f w.r.t S (shortly, (CLRf)property w.r.t to S) if there exist sequences {ξn} and {ζn} in Θ and Ω1, Ω2 ∈ CB(Θ) such that, for some u ∈ Θ, we have limn→∞Sξn = Ω1, limn→∞Tζn = Ω2, and limn→∞fξn = limn→∞gζn = fu ∈ Ω1 ∩ Ω2.
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