PHP isn't client-side, so you can't call a function without having it reload the page... you could use javascript, but you can't call a PHP function with it, you'll have to do it in Javascript.
You could obviously submit your form with a hidden variable like the following:
Add this to your form:
<input type="hidden" name="submitted" value="yes">
Then on your next page:
<?php if($submitted == "yes"){yourFunction();} ?>
If you changed your form's action to:
action="<?php echo $PHP_SELF;?>"
Then it'll submit the page to itself (basically just reloading the form but including the variables.
I still think you'd be best using Javascript for what you're doing, but we don't really know what you are doing.