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Monotonic solutions for quadratic integral equations

100%
Cichoń M., Metwali M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
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nr 2
157-171
EN
Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
2
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Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

100%
Eshmatov B., Karimov E.
Open Mathematics
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2007
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tom 5
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nr 4
741-750
EN
In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.
3
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Common fixed point results of four mappings in ordered partial metric spaces

72%
Nazir T., Silvestrov S., Abbas M.
Waves, Wavelets and Fractals
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2016
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tom 2
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nr 1
EN
On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature.We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.
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