Solutions of a Class of Operator Equation in Continuous Function Spaces and Several Applications

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DOI: https://doi.org/10.28924/2291-8639-24-2026-120
Published: Apr 20, 2026
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Chengbo Zhai, Yong Zhou, Solutions of a Class of Operator Equation in Continuous Function Spaces and Several Applications, Int. J. Anal. Appl., 24 (2026), 120.

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Chengbo Zhai, Yong Zhou

Abstract

This paper investigates an operator equation of the form \(x = (Ax^s)^{1/s} + x_0,\) where \(A\) is a linear operator defined in continuous function spaces, \(s>1\) is a real number and \(x_0\) is a positive continuous function. We transform it into a fixed point problem and establish the existence and uniqueness of solutions by using some results for increasing concave operators in the interior of cones. Moreover, we give several applications in Caputo fractional differential problems, recursive preferences and wealth-consumption ratio.

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