Just to make sure, did you insert the which compile.sh inside /home/vinoth/funtions.sh? Because path may be modified within function. Once you are there print the full path too (from within that function). If your path contains the dot early then ANY compile.sh script in script's current dir will be executed first. So within the function print PWD as well at the moment of attempted execution.

which compile.shgives me correct path of compile.sh, that path is available in PATH variable.

Without more data it's going to be hard to guess what's happening in that case. Here's an SSCCE which might help:

cd /tmp
cat > foo.sh <<EOT
#!/bin/sh
echo Relative path
./bar.sh
echo Absolute path
/tmp/bar.sh
echo No path
bar.sh
EOT
cat > bar.sh <<EOT
#!/bin/sh
echo bar running as \$0
EOT
chmod 0755 foo.sh bar.sh
sudo chown root bar.sh
sudo cp -p bar.sh /usr/local/bin
./foo.sh
[download]

Running this locally (not on Solaris!) gives this expected output:

Relative path
bar running as ./bar.sh
Absolute path
bar running as /tmp/bar.sh
No path
bar running as /usr/local/bin/bar.sh
[download]

If you see the same, then you'll need to determine what's different about functions.sh and compile.sh compared to foo.sh and bar.sh. Don't forget to remove bar.sh from /usr/local/bin when you're done. Good luck.