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Fixed point in Banach *-algebras with an application to functional integral equation of fractional order

Nilakshi Goswami|Goutam Das
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.12|한국수학논문집 (Korean Journal of Mathematics)|제32권 제4호|pp. 615-628

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키워드

Schauder's fixed point theoremfractional integral equationBanach *-algebra.
주제분류수학

초록

In this paper, we investigate the solvability of an operator equation involving four operators in the setting of Banach *-algebras using Schauder's fixed point theorem. Moreover, we have given an application of our result to the following functional integral equation of fractional order: $$ \xi(t)=g(t,\xi(\psi_1(t)))I^{\alpha} f_1(t,I^{\beta}u(t,\xi(\psi_2(t))))+h(t,\xi(\psi_3(t)))I^{\gamma}f_2(t,I^{\delta}v(t,\xi^*(\psi_4(t)))) $$ for proving the existence as well as the uniqueness of the solution in Banach *-algebras under some generalized conditions.

Abstract

In this paper, we investigate the solvability of an operator equation involving four operators in the setting of Banach *-algebras using Schauder's fixed point theorem. Moreover, we have given an application of our result to the following functional integral equation of fractional order: $$ \xi(t)=g(t,\xi(\psi_1(t)))I^{\alpha} f_1(t,I^{\beta}u(t,\xi(\psi_2(t))))+h(t,\xi(\psi_3(t)))I^{\gamma}f_2(t,I^{\delta}v(t,\xi^*(\psi_4(t)))) $$ for proving the existence as well as the uniqueness of the solution in Banach *-algebras under some generalized conditions.

참고문헌 (33)

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