SMA X AND SMT Y ON VISUAL APCHS TO MULTIPLE RWY OPS PARALLEL RWYS HAD LTSS. SYS ERROR.

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I HAD CLRED SMA X TOWARD A VISUAL APCH FOR RWY 35L TO ENTER A R BASE FROM A POS 6-7 MI E OF THE ARPT. SMT Y HAD BEEN ON VECTORS FOR AN ILS; WHEN AT APPROX 12 MI S OF THE ARPT SMT Y SAW THE ARPT AND I CLRED HIM FOR A VISUAL APCH STRAIGHT IN TO RWY 35R. SEVERAL OTHER ACFT WERE ON FREQ ON VECTORS TO BOTH DYERS AFB AND ABI REGIONAL DRAWING MY ATTN AWAY. BOTH ABOVE ACFT WERE INITIALLY DIVERGING TOWARD THEIR RESPECTIVE OFFSET PARALLEL RWYS BUT WOULD CONVERGE CLOSE TO THE ARPT. SMA X WIDENED OUT HIS R BASE TO RWY 35R AND WHEN I NOTICED THAT FACT THE 2 COURSES APPEARED TO BE CONVERGING. I ISSUED TFC TO SMT Y AND WHEN HE REPLIED NO CONTACT; I TURNED HIM OUT STRAIGHT WBOUND IN AN EFFORT TO MAINTAIN PRESCRIBED 3 MI SEPARATION AFTER THE 'DIVERGING COURSES' RULE NO LONGER APPLIED. SMT Y SAW SMA X AT THE APPROX POINT WHERE BOTH JOINED THEIR RESPECTIVE FINAL APCH COURSES. A RAPCON SUPVR WAS WATCHING AS THE SIT DEVELOPED. HE ADVISED ME THAT PRESCRIBED LATERAL SEPARATION WAS LOST AND MY 3 MI WAS ACTUALLY 2 1/2 AND HE RPTED IT TO HIGHER AUTHORITIES. IN RETROSPECT; I SHOULD HAVE ISSUED A HDG FOR SMT Y TO JOIN FINAL FOR RWY 35L AT THE TIME I CHANGED HIM FROM ILS TO VISUAL APCH. THAT WOULD'VE INSURED THAT IN THE EVENT I WAS DISTRACTED; THEY WOULD NOT HAVE BEGUN TO CONVERGE AS SMT Y EXECUTED A SHALLOW ANGLE TOWARD RWY 35L FINAL.