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I tried to update quantity for each product in shopping cart, but it's not working for every product in list separately.
As I understand your query, it update the quantity of all items in cart because you don't say which item (in cart) you want to update.
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Question: you use the user public ip as identification, but what happen when 2 users working in same company have same public ip ?
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$update_qty = "update cart set qty='$qty' where ip_add='$ip'";
Not a solution to your question, but another problem you have.
Never build an SQL query by concatenating strings. Sooner or later, you will do it with user inputs, and this opens door to a vulnerability named "SQL injection", it is dangerous for your database and error prone.
A single quote in a name and your program crash. If a user input a name like "Brian O'Conner" can crash your app, it is an SQL injection vulnerability, and the crash is the least of the problems, a malicious user input and it is promoted to SQL commands with all credentials.
SQL injection - Wikipedia[
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SQL Injection[
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SQL Injection Attacks by Example[
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PHP: SQL Injection - Manual[
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SQL Injection Prevention Cheat Sheet - OWASP[
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