Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra
Abstract
:1. Introduction
2. Preliminaries
- (N1)
- and
- (N2)
- (N3)
- for all and
- (A1)
- (A2)
- (A3)
- (A4)
- for all and scalars
- (i)
- for all we have that implies that X is precompact.
- (ii)
- the family ker is non-empty, and ker
- (iii)
- (iv)
- (v)
- where is the convex closure of set
- (vi)
- for
- (vii)
- if for and , then
3. Main Result
- (1)
- The functions , and are continuous, and there exist nonnegative constants such that:
- (2)
- Let be continuous functions such that:
- (3)
- The functions are continuous functions from to
- (4)
- Furthermore, for
4. An Illustrative Example
5. An Iterative Algorithm Created by a Coupled Semi-Analytic Method to Find the Solution of the Integral Equation
Algorithm 1. Algorithm of calculating |
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Srivastava, H.M.; Das, A.; Hazarika, B.; Mohiuddine, S.A. Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra. Symmetry 2019, 11, 674. https://doi.org/10.3390/sym11050674
Srivastava HM, Das A, Hazarika B, Mohiuddine SA. Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra. Symmetry. 2019; 11(5):674. https://doi.org/10.3390/sym11050674
Chicago/Turabian StyleSrivastava, Hari M., Anupam Das, Bipan Hazarika, and S. A. Mohiuddine. 2019. "Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra" Symmetry 11, no. 5: 674. https://doi.org/10.3390/sym11050674