The Integral Expansions of Arbitrary Functions connected with Integral Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 169-185 ◽  
Author(s):  
J. Hyslop
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Point Of View ◽  
General Treatment ◽  
Integral Equation Theory

The following paper aims at a more general treatment than has hitherto been given, of the integral expansions of arbitrary functions, from the point of view of integral equation theory.

scholarly journals Convolution, fixed point, and approximation in Stieltjes-Volterra integral equations

1972 ◽  
Vol 14 (2) ◽  
pp. 182-199 ◽  
Author(s):  
Carl W. Bitzer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
The Other ◽  
Integral Equation Theory ◽  
Identity Function ◽  
Convolution Integrals

This paper focuses primarily on two aspects of Stieltjes-Volterra integral equation theory. One is a theory for convolution integrals — that is, integrals of the form — and the other is a fixed point theorem for a mapping which is induced by an integral equation. Throughout the paper I will denote the identity function whose range of definition should be clear from the context and all integrals will be left integrals, written , whose simplest approximating sum is [f(b) – f(a)]·g(a) and whose value is the limit of approximating sums with respect to successive refinements of the interval. Also, N will denote the set of elements of a complete normed ring with unity 1 and S will denote a set linearly ordered by ≦.

scholarly journals On a Functional Integral Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1321
Author(s):  
Daniela Marian ◽  
Sorina Anamaria Ciplea ◽  
Nicolaie Lungu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Functional Integral ◽  
Point Of View ◽  
Hammerstein Integral Equation ◽  
Stability Point ◽  
The Stability ◽  
Rassias Stability ◽  
Differential And Integral Equations

In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, integral inequalities, monotony and Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential and integral equations and those are approached in the stability point of view. In the literature, Fredholm, Volterra and Hammerstein integrals equations with symmetric kernels are studied. Our results can be applied as particular cases to these equations.

Comparison of atomic force microscopy force curve and solvation structure studied by integral equation theory

2021 ◽  
Vol 154 (16) ◽  
pp. 164702
Author(s):  
Kota Hashimoto ◽  
Ken-ichi Amano ◽  
Naoya Nishi ◽  
Hiroshi Onishi ◽  
Tetsuo Sakka
Keyword(s):  
Integral Equation ◽  
Atomic Force Microscopy ◽  
Integral Equation Theory ◽  
Force Curve ◽  
Force Microscopy ◽  
Atomic Force ◽  
Solvation Structure
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