scholarly journals A family of measures of noncompactness in the space Lploc(ℝN) and its application to some nonlinear convolution type integral equations

2019 ◽  
Vol 6 (1) ◽  
pp. 1592276
Author(s):  
Hojjatollah Amiri Kayvanloo ◽  
Mahnaz Khanehgir ◽  
Reza Allahyari ◽  
Hari M. Srivastava
Keyword(s):  
Integral Equations ◽  
Convolution Type ◽  
Measures Of Noncompactness ◽  
Type Integral

scholarly journals Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

2021 ◽  
Vol 37 (3) ◽  
pp. 407-416
Author(s):  
SHAHRAM BANAEI ◽  
◽  
VAHID PARVANEH ◽  
MOHAMMAD MURSALEEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Fréchet Space ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Type Integral ◽  
Systems Of Integral Equations

"In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $L^\infty(\mathfrak{G})$ (where $\mathfrak{G}\subseteq \mathbb{R}^{\omega}$) have been proved. We handle our obtained consequences to inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example."

scholarly journals On an integral transform

1986 ◽  
Vol 9 (2) ◽  
pp. 283-292 ◽  
Author(s):  
D. Naylor
Keyword(s):  
Bessel Function ◽  
Integral Equations ◽  
Inversion Formula ◽  
Integral Transform ◽  
Zero Order ◽  
Convolution Type ◽  
Type Integral ◽  
Related Integral

This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.

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