Fixed point theorem via measure of noncompactness and application to Volterra integral equations in Banach algebras

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Kumar Nashine Hemant; REZAEI ROSHAN JAMAL

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Journal: JOURNAL OF MATHEMATICAL EXTENSION Year:2019 | Volume:13 | Issue:4 Page(s): 91-116

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Title

Fixed point theorem via measure of noncompactness and application to Volterra integral equations in Banach algebras

Author(s)

Kumar Nashine Hemant | REZAEI ROSHAN JAMAL | Issue Writer Certificate

Keywords

Measures of noncompactness

Darbo’s fixed point theorem

coupled fixed point

integral equations

Abstract

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space and derive some basic Darbo type fixed and coupled fixed point results. This work includes and extends the results of Falset and Latrach[ Falset, J. G., Latrach, K.: On Darbo-Sadovskii's fixed point theorems type for abstract measures of (weak) noncompactness, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 797-812. ] The results are also correlated with the classical generalized Banach fixed point theorems. Also we show the applicability of obtained results to the Volterra integral equations in Banach algebras.

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APA: Copy

Kumar Nashine, Hemant, & REZAEI ROSHAN, JAMAL. (2019). Fixed point theorem via measure of noncompactness and application to Volterra integral equations in Banach algebras. JOURNAL OF MATHEMATICAL EXTENSION, 13(4), 91-116. SID. https://sid.ir/paper/730792/en

Vancouver: Copy

Kumar Nashine Hemant, REZAEI ROSHAN JAMAL. Fixed point theorem via measure of noncompactness and application to Volterra integral equations in Banach algebras. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2019;13(4):91-116. Available from: https://sid.ir/paper/730792/en

IEEE: Copy

Hemant Kumar Nashine, and JAMAL REZAEI ROSHAN, “Fixed point theorem via measure of noncompactness and application to Volterra integral equations in Banach algebras,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 13, no. 4, pp. 91–116, 2019, [Online]. Available: https://sid.ir/paper/730792/en

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