Solution of integral equations via coupled fixed point theorems in F-complete metric spaces
- Authors
- Mani, Gunaseelan; Gnanaprakasam, Arul Joseph; Lee, Jung Rye; Park, Choonkil
- Issue Date
- Jul-2021
- Publisher
- DE GRUYTER POLAND SP Z O O
- Keywords
- orthogonal set; orthogonal metric space; orthogonal continuous; orthogonal preserving; orthogonal F-contraction; coupled fixed point
- Citation
- OPEN MATHEMATICS, v.19, no.1, pp.1223 - 1230
- Indexed
- SCIE
SCOPUS
- Journal Title
- OPEN MATHEMATICS
- Volume
- 19
- Number
- 1
- Start Page
- 1223
- End Page
- 1230
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/141474
- DOI
- 10.1515/math-2021-0075
- ISSN
- 2391-5455
- Abstract
- The concept of coupled F-orthogonal contraction mapping is introduced in this paper, and some coupled fixed point theorems in orthogonal metric spaces are proved. The obtained results generalize and extend some of the well-known results in the literature. An example is presented to support our results. Furthermore, we apply our result to obtain the existence theorem for a common solution of the integral equations: {zeta(nu) = partial derivative(nu) + integral(m)(0) Xi(nu, beta)Omega(beta, zeta(beta), xi(beta))d beta, nu is an element of [0, H], xi(nu) = partial derivative(nu) + integral(m)(0) Xi(nu, beta)Omega(beta, xi(beta), zeta(beta))d beta, nu is an element of [0, H], where (a) partial derivative : m -> R and Omega : m x R x R -> R are continuous; (b) Xi : m x m is continuous and measurable at beta is an element of m, for all nu is an element of m; (c) Xi(nu, beta) >= 0, for all nu, beta is an element of m and integral(H)(0) Xi(nu, beta)d beta <= 1, for all nu is an element of m.
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