Abstract
<abstract><p>In this paper, we establish a modified proximal point algorithm for solving the common problem between convex constrained minimization and modified variational inclusion problems. The proposed algorithm base on the proximal point algorithm in <sup>[<xref ref-type="bibr" rid="b19">19</xref>]</sup> and the method of Khuangsatung and Kangtunyakarn in <sup>[<xref ref-type="bibr" rid="b21">21</xref>]</sup> by using suitable conditions in Hilbert spaces. The proposed algorithm is not only presented in this article; however has also been demonstrated to generate a robust convergence theorem. The proposed algorithm could be used to solve image restoration problems where the images have suffered a variety of blurring operations. Additionally, we contrast the signal-to-noise ratio (SNR) of the proposed algorithm against that of Khuangsatung and Kangtunyakarn's method in <sup>[<xref ref-type="bibr" rid="b21">21</xref>]</sup> in order to compare image quality.</p></abstract>
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