diff --git a/tests/lib/rules/function-component-definition.js b/tests/lib/rules/function-component-definition.js
index 6fd8269a1f..f75338592f 100644
--- a/tests/lib/rules/function-component-definition.js
+++ b/tests/lib/rules/function-component-definition.js
@@ -68,6 +68,32 @@ ruleTester.run('function-component-definition', rule, {
   }, {
     code: 'var Foo = React.memo(function Foo() { return <p/> })',
     options: [{namedComponents: 'function-declaration'}]
+  }, {
+    // shouldn't trigger this rule since functions stating with a lowercase
+    // letter are not considered components
+    code: `
+    const selectAvatarByUserId = (state, id) => {
+      const user = selectUserById(state, id)
+      return null
+    }
+    `,
+    options: [{namedComponents: 'function-declaration'}]
+  }, {
+    // shouldn't trigger this rule since functions stating with a lowercase
+    // letter are not considered components
+    code: `
+      function ensureValidSourceType(sourceType: string) {
+        switch (sourceType) {
+          case 'ALBUM':
+          case 'PLAYLIST':
+            return sourceType;
+          default:
+            return null;
+        }
+      }
+    `,
+    options: [{namedComponents: 'arrow-function'}],
+    parser: parsers.TYPESCRIPT_ESLINT
   }, {
     code: 'function Hello(props: Test) { return <p/> }',
     options: [{namedComponents: 'function-declaration'}],
diff --git a/tests/lib/rules/prop-types.js b/tests/lib/rules/prop-types.js
index bf9926c382..3ae7c0bd86 100755
--- a/tests/lib/rules/prop-types.js
+++ b/tests/lib/rules/prop-types.js
@@ -2504,7 +2504,27 @@ ruleTester.run('prop-types', rule, {
         }
       `,
       parser: parsers.TYPESCRIPT_ESLINT
-    }
+    },
+    // shouldn't trigger this rule since functions stating with a lowercase
+    // letter are not considered components
+    `
+      function noAComponent(props) {
+        return <div>{props.text}</div>
+      }
+    `,
+    // shouldn't trigger this rule for 'render' since functions stating with a lowercase
+    // letter are not considered components
+    `
+      const MyComponent = (props) => {
+        const render = () => {
+          return <test>{props.hello}</test>;
+        }
+        return render();
+      };
+      MyComponent.propTypes = {
+        hello: PropTypes.string.isRequired,
+      };
+    `
   ],
 
   invalid: [