Banach fixed point theorem for fractional integral contraction.
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| Title: | Banach fixed point theorem for fractional integral contraction. |
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| Authors: | Ayoob, Irshad1 (AUTHOR) iayoub@psu.edu.sa |
| Source: | Fixed Point Theory & Algorithms for Sciences & Engineering. 12/22/2025, Vol. 2025 Issue 1, p1-16. 16p. |
| Subjects: | Fixed point theory, Contraction operators, Metric spaces, Fractional integrals |
| Abstract: | One of the most intensively studied and generalized results in metric fixed point theory is Branciari's fixed point theorem, which asserts that in a complete metric space (M , ρ) , a mapping T : M → M satisfying ∫ 0 ρ (T x , T y) ω (t) d t ≤ c ∫ 0 ρ (x , y) ω (t) d t for some ω : [ 0 , ∞) → [ 0 , ∞) , c ∈ (0 , 1) , and all x , y ∈ M , admits a unique fixed point x ∗ ∈ M. This reduces to Banach fixed theorem when ω (t) = 1. We extend this to Riemann–Liouville fractional integral contractions, proving the existence of a fixed point for T under 1 Γ (α) ∫ 0 ρ (T x , T y) (ρ (T x , T y) − t) α − 1 φ (t) d t ≤ c ⋅ 1 Γ (α) ∫ 0 ρ (x , y) (ρ (x , y) − t) α − 1 φ (t) d t , which recovers Branciari's integral condition for α = 1. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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