On a Nonlinear Integral Equation for Population Growth Problems

1975 ◽  
Vol 6 (2) ◽  
pp. 312-317 ◽  
Author(s):  
Fred Brauer
Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht

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.


2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas

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.


Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen

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 .


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nurgali K. Ashirbayev ◽  
Józef Banaś ◽  
Raina Bekmoldayeva

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.


1980 ◽  
Vol 98 (1) ◽  
pp. 161-169 ◽  
Author(s):  
Jean-Marc Vanden-Broeck ◽  
Joseph B. Keller

A new family of finite-amplitude periodic progressive capillary waves is presented. They occur on the surface of a fluid of infinite depth in the absence of gravity. Each pair of adjacent waves touch at one point and enclose a bubble at pressure P. P depends upon the wave steepness s, which is the vertical distance from trough to crest divided by the wavelength. Previously Crapper found a family of waves without bubbles for 0 [les ] s [les ] s* = 0·730. Our solutions occur for all s > s** = 0·663, with the trough taken to be the bottom of the bubble. As s → ∞, the bubbles become long and narrow, while the top surface tends to a periodic array of semicircles in contact with one another. The solutions were obtained by formulating the problem as a nonlinear integral equation for the free surface. By introducing a mesh and difference method, we converted this equation into a finite set of nonlinear algebraic equations. These equations were solved by Newton's method. Graphs and tables of the results are included. These waves enlarge the class of phenomena which can occur in an ideal fluid, but they do not seem to have been observed.


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