Cross-Platform Mobile App Development

I need a mobile app developed for both iOS and Android platforms. The app's primary purpose is not limited to e-commerce, social networking, or productivity; it falls under 'other' categories.

Essential features should include:
- User authentication
- Push notifications
- In-app purchases

Ideal skills and experience:
- Proven experience in cross-platform mobile app development
- Strong knowledge of user authentication protocols
- Experience with implementing push notifications and in-app purchase systems
- Familiarity with both iOS and Android design guidelines
- Ability to deliver a user-friendly and secure app

Please provide examples of similar work done and estimated timelines.