Existence of fixed points for pairs of mappings and application to Urysohn integral equations

2017/09/09 by Deepak Kumar, Kumar, Deepak, Sumit Chandok +1
Mathematics · #47H10 #54H25 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Functional Equations Stability Results #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1709.02913

openalex publication_date 2017/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish some common fixed point results for two pairs of weakly compatible mappings in the setting of C-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of a common solution of the system of the Urysohn integral equations: x(t)=ψ_i(t)+∫_a^bK_i(t,s,x(s))ds where i=1, 2, 3, 4, a,b∈ ℝ with a≤ b, t∈ [a,b], x, ψ_i∈ C([a,b],ℝⁿ) and K_i:[a,b]× [a,b]× ℝⁿ→ ℝⁿ is a mapping for each i=1, 2, 3, 4.

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