About 4 years ago, before I started my PhD, I published a paper which used a method to improve an existing result. There were 2 papers on the existing result and method which I used for my work and appropriately cited. A couple of days ago I discovered another paper on arXiV by the same authors, which dealt with the same problem, which I did not cite for reasons I can't remember. Also, I realize that they address the same problem that I worked on, in a small sub-section of their arXiV paper.

Based on the references that I used, I gathered that the problem I solved had not been looked into in the works of theirs that I cited and made a statement about this fact. Although, the method that I have used is different from theirs, it still makes my statement erroneous. I feel that I am thoroughly screwed and the damage is irreparable. How do I go about resolving this issue? I am willing to let everybody involved on my paper know about it, apart from the authors whose papers that I have not cited. Is there anything more to be done?

About 4 years ago, before I started my PhD, I published a paper which used a method to improve an existing result. There were 2 papers on the existing result and method which I used for my work and appropriately cited. A couple of days ago I discovered another paper on arXiV by the same authors, which dealt with the same problem, which I did not cite for reasons I can't remember. Also, I realize that they address the same problem that I worked on, in a small sub-section of their arXiV paper.

Based on the references that I used, I gathered that the problem I solved had not been looked into in the works of theirs that I cited and made a statement about this fact. Although, the method that I have used is different from theirs, it still makes my statement erroneous. I feel that I am thoroughly screwed and the damage is irreparable. How do I go about resolving this issue? I am willing to let everybody involved on my paper know about it, including the authors whose papers that I have not cited. Is there anything more to be done?

About 4 years ago, before I started my PhD, I published a paper which used a method to improve an existing result. There were 2 papers on the existing result and method which I used for my work and appropriately cited. A couple of days ago I discovered another paper on arXiV which dealt with the same problem, which I did not cite for reasons I can't remember. Also, I realize that they address the same problem that I worked on, in a small sub-section of their arXiV paper.

Based on the references that I used, I gathered that the problem I solved had not been looked into in the works of theirs that I cited and made a statement about this fact. Although, the method that I have used is different from theirs, it still makes my statement erroneous. I feel that I am thoroughly screwed and the damage is irreparable. How do I go about resolving this issue? I am willing to let everybody involved on my paper know about it, apart from the authors whose papers that I have not cited. Is there anything more to be done?

About 4 years ago, before I started my PhD, I published a paper which used a method to improve an existing result. There were 2 papers on the existing result and method which I used for my work and appropriately cited. A couple of days ago I discovered another paper on arXiV by the same authors, which dealt with the same problem, which I did not cite for reasons I can't remember. Also, I realize that they address the same problem that I worked on, in a small sub-section of their arXiV paper.

Based on the references that I used, I gathered that the problem I solved had not been looked into in the works of theirs that I cited and made a statement about this fact. Although, the method that I have used is different from theirs, it still makes my statement erroneous. I feel that I am thoroughly screwed and the damage is irreparable. How do I go about resolving this issue? I am willing to let everybody involved on my paper know about it, apart from the authors whose papers that I have not cited. Is there anything more to be done?