scholarly journals On Solutions of a Nonlinear Erdélyi-Kober Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nurgali K. Ashirbayev ◽  
Józef Banaś ◽  
Raina Bekmoldayeva
Keyword(s):  
Integral Equation ◽  
Nonlinear Integral Equation ◽  
Special Case ◽  
Stieltjes Type

We conduct some investigations concerning the solvability of a nonlinear integral equation of Erdélyi-Kober type. To facilitate our study we will first consider a nonlinear integral equation of Volterra-Stieltjes type. Since the mentioned Erdélyi-Kober integral equation turns out to be a special case of that of Volterra-Stieltjes type, we can apply the obtained results to the Erdélyi-Kober integral equation. Examples illustrating the obtained results will be also included.

scholarly journals Solvability of an Integral Equation of Volterra-Wiener-Hopf Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Nurgali K. Ashirbayev ◽  
Józef Banaś ◽  
Agnieszka Dubiel
Keyword(s):  
Integral Equation ◽  
Nonlinear Integral Equation ◽  
Bounded Solution ◽  
Finite Limit ◽  
Special Case ◽  
Class Of Functions ◽  
Stieltjes Type

The paper presents results concerning the solvability of a nonlinear integral equation of Volterra-Stieltjes type. We show that under some assumptions that equation has a continuous and bounded solution defined on the interval0,∞and having a finite limit at infinity. As a special case of the mentioned integral equation we obtain an integral equation of Volterra-Wiener-Hopf type. That fact enables us to formulate convenient and handy conditions ensuring the solvability of the equation in question in the class of functions defined and continuous on the interval0,∞and having finite limits at infinity.

scholarly journals Withdrawal of layered fluid through a line sink in a porous medium

1996 ◽  
Vol 38 (2) ◽  
pp. 240-254 ◽  
Author(s):  
H. Zhang ◽  
G. C. Hocking
Keyword(s):  
Integral Equation ◽  
Porous Medium ◽  
Exact Solutions ◽  
Flow Rate ◽  
Nonlinear Integral Equation ◽  
Line Sink ◽  
Different Depths ◽  
Special Case ◽  
Sink Location ◽  
Layered Fluid

AbstractThe flow induced when fluid is withdrawn through a line sink from a layered fluid in a homogeneous, vertically confined porous medium is studied. A nonlinear integral equation is derived and solved numerically. For a given sink location, the shape of the interface can be determined for various values of the flow rate. The results are compared with exact solutions obtained using hodograph methods in a special case. It is found that the cusped and coning shapes of the interface can be accurately obtained for the sink situated at different depths in the fluid and the volume of flow into the sink per unit of time.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

scholarly journals A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Convex Sets ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Modular Space ◽  
Ordinate Axis ◽  
Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

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