Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

Hammad, Hasanen A.; Aydi, Hassen; Park, Choonkil

doi:10.3934/math.2022501

Cited by 7 publications

(1 citation statement)

References 31 publications

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“…Rasham et al [35] proved an expressive fixed point results for sufficient conditions to solve two systems of nonlinear integral equations. For further fixed point results with applications related to integral equations (see [12,18,27,33,41]). Theorem 4.1.…”

Section: Application For Nonlinear Voltera Type Integral Equationsmentioning

confidence: 99%

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-metric Spaces with Applications

Rasham¹,

Nazam²,

Aydi³

et al. 2022

Preprint

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In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

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Section: Application For Nonlinear Voltera Type Integral Equationsmentioning

confidence: 99%

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-metric Spaces with Applications

Rasham¹,

Nazam²,

Aydi³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Existence of Fixed Points for a Class of Decreasing Operators with Parameter and Applications

Tian

2022

Journal of Mathematics

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This paper studies the existence of fixed points for a class of decreasing operators with parameter in real Banach spaces. The existence theorems of fixed point are obtained as when the parameter is increasing, there will still be a large fixed point. These results have reduced the requirements of convexity, compactness, and lattice structure of spaces. By this new method, the existence of solutions for a class of second-order differential equations with parameter in infinite intervals is studied.

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Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-Metric Spaces with Applications

et al. 2022

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In this paper, we introduce a generalized Δ-implicit locally contractive condition and give some examples to support it and show its significance in fixed point theory. We prove that the mappings satisfying the generalized Δ-implicit locally contractive condition admit a common fixed point, where the ordered multiplicative GM-metric space is chosen as the underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show the existence of solutions to a system of nonlinear—Volterra type—integral equations.

show abstract

Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

Cited by 7 publications

References 31 publications

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-metric Spaces with Applications

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-metric Spaces with Applications

Existence of Fixed Points for a Class of Decreasing Operators with Parameter and Applications

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-Metric Spaces with Applications

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