Positive solutions of semi-positone Hammerstein integral equations and applications

Zhao, Zengqin

doi:10.1016/j.amc.2012.09.009

Cited by 13 publications

(11 citation statements)

References 7 publications

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“…which proves that verifies contraction condition (36) in Corollary 4. Next, we consider a monotone nondecreasing sequence { } ⊂ converging to ∈ .…”

Section: Journal Of Function Spacessupporting

confidence: 76%

“…Recently, a new version of the context of ordered metric spaces has been proved by Harjani and Sadarangani in [12]. We refer the readers to [36][37][38][39][40][41] for more related works.…”

Section: Definition a Mappingmentioning

confidence: 99%

“…Journal of Function Spaces Note that, in (36), is not necessary to be an altering distance function.…”

Section: Corollarymentioning

confidence: 99%

See 2 more Smart Citations

New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

Liu

Mao

Shi

2018

Journal of Function Spaces

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We consider the existence of a coupled fixed point for mixed monotone mapping F:X×X→X satisfying a new contractive inequality which involves an altering distance function in partially ordered metric spaces. We also establish some uniqueness results for coupled fixed points, as well as the existence of fixed points of mixed monotone operators. The presented results generalize and develop some existing results. In addition to an example as well as an application, we establish some uniqueness results for a system of integral equations.

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“…which proves that verifies contraction condition (36) in Corollary 4. Next, we consider a monotone nondecreasing sequence { } ⊂ converging to ∈ .…”

Section: Journal Of Function Spacessupporting

confidence: 76%

Section: Definition a Mappingmentioning

confidence: 99%

See 1 more Smart Citation

New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

Liu

Mao

Shi

2018

Journal of Function Spaces

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“…4. We should point out that Hammerstein integral equations can be ascribed to general nonlinear operator equations discussed in this paper [18].…”

Section: Introductionmentioning

confidence: 88%

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

Sang

Ren

2019

Bound Value Probl

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In this paper, by studying the solutions of the abstract operator equation A(x, x) + B(x, x) + e = x on ordered Banach spaces, where A, B are two mixed monotone operators and e ∈ P with θ ≤ e ≤ h, we prove a class of boundary value problems on elastic beam equation to have a unique solution. Furthermore, we also apply our abstract result to establish the existence and uniqueness theorem of nontrivial solutions for nonlinear fractional boundary value problems. The iterative sequences to approximate unique solutions for the above two classes of problems are also obtained.

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“…Partial order method is discussed and applied greatly in mathematics, and the conclusion on the partial order is becoming a very complete system [13][14][15][16][17][18][19][20][21][22][23]. But few scholars study the fixed point and extreme value theorems on incomplete preference set.…”

Section: Existence Theorems For Fixed Point On Incomplete Preference mentioning

confidence: 99%

Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference

2018

Journal of Function Spaces

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To prove the existence of Nash equilibrium by traditional ways, a common condition that the preference of players must be complete has to be considered. This paper presents a new method to improve it. Based on the incomplete preference corresponding to equivalence class set being a partial order set, we translate the incomplete preference problems into the partial order problems. Using the famous Zorn lemma, we get the existence theorems of fixed point for noncontinuous operators in incomplete preference sets. These new fixed point theorems provide a new way to break through the limitation. Finally, the existence of generalized Nash equilibrium is strictly proved in the n-person noncooperative games under incomplete preference.

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Positive solutions of semi-positone Hammerstein integral equations and applications

Cited by 13 publications

References 7 publications

New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference

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