scholarly journals New classes of condensing operators and application to solvability of singular integral equations

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 843-860
Author(s):  
A. Aghajani ◽  
M. Aliaskari ◽  
D. O’Regan
Keyword(s):  
Banach Algebra ◽  
Fixed Points ◽  
Banach Spaces ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Condensing Operators ◽  
The Way

In this paper, we introduce the notion of Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. In order to pave the way for a study the solvability of some classes of singular integral equations in the Banach algebra C[a,b], we provide some results for the existence of fixed points for such condensing operators. An example is presented to show the applicability of the results.

scholarly journals On multi-singular integral equations involving n weakly singular kernels

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1323-1333 ◽  
Author(s):  
Sales Nabavi ◽  
O. Baghani
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Singular Integral ◽  
Applied Mathematics ◽  
Uniform Space ◽  
Singular Integral Equations ◽  
Restrictive Assumption ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels

We deal with some sources of Banach spaces which are closely related to an important issue in applied mathematics i.e. the problem of existence and uniqueness of the solution for the very applicable weakly singular integral equations. In the classical mode, the uniform space (C[a,b], ||.||?) is usually applied to the related discussion. Here, we apply some new types of Banach spaces, in order to extend the area of problems we could discuss. We consider a very general type of singular integral equations involving n weakly singular kernels, for an arbitrary natural number n, without any restrictive assumption of differentiability or even continuity on engaged functions. We show that in appropriate conditions the following multi-singular integral equation of weakly singular type has got exactly a solution in a defined Banach space x(t) = ?p,i=1 ?i/?(^?i) ?t,0 fi(s,x(s)) (tn-tn-1)1-?i,n...(t1-s)1-?i,1 dt + ?(t). In particular we consider the famous fractional Langevin equation and by the method we could extend the region of variations of parameter ?+ ? from interval [0,1) in the earlier works to interval [0,2).

scholarly journals Existence of Tripled Fixed Points for a Class of Condensing Operators in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vatan Karakaya ◽  
Nour El Houda Bouzara ◽  
Kadri Doğan ◽  
Yunus Atalan
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
General System ◽  
Nonlinear Integral Equations ◽  
Condensing Operators

We give some results concerning the existence of tripled fixed points for a class of condensing operators in Banach spaces. Further, as an application, we study the existence of solutions for a general system of nonlinear integral equations.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna
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