These arm strengthening exercises are variations of push ups that can make it easier to gradually increase arm strength because they are progressive. They use various leg and body positions to make push up exercises easier or harder as required.
For all arm strengthening exercises where the arms support some portion of the weight of your body, focus first on stabilizing your shoulder blades relative to your ribcage.
To make scapular stability easier to learn first focus on scapular awareness.
To stabilize your scapula in the following push-up like arm strengthening exercises work at protracting your shoulder blades.
The idea isn't to keep your shoulder blades protracted to maximum, but to vary (or control) the amount of protraction depending on the amount of bend in your elbows.
This one-armed push up exercise can be made easier by starting with both your knees and your hip resting on the floor.
Starting with a straight elbow, practice shoulder blade awareness by protracting so that your ribcage pushes away from the floor, then relaxing the protraction while keeping the elbow straight.
Notice the changes in the feeling of tension around your shoulder blade (between it and your ribcage) as you repeat this exercise. Pay particular attention to the feeling of tension that is created when you protract. Memorize this sensation.
When bending and straightening the elbow to strengthen the arm you can start with the elbow straight or you can start with the elbow bent and your torso on the floor.
Starting with elbow straight, first protract your shoulder, then keep the feeling of protraction as you bend your elbow. The actual position of your shoulder blade will change as you bend your elbow. That's fine, however do work at maintaining the feeling of protraction.
If you can only go so far down, that's fine. Straighten the arm and repeat. If you get too tired to keep the protraction, then rest by switching sides.
Starting from the floor do the same thing, protract, then knee the protraction as you work at straightening your elbow.
Low lunge can also be used as an arm strengthening exercise if you are flexible enough. With the left leg forwards, focus on strengthening your right arm. So that the work of your right arm is easier, press down into the floor with your left foot. Your left thigh or hip should feel strong.
As with the previous exercise, protract your shoulder blades. Then gradually bend your elbows to sink your chest down. Keep the protraction and in addition keep your front leg active.
In this arm strengthening exercise you'll be limited by the flexibility of your front leg. But you may find that you can strengthen your arms and legs together and in the process help improve hip flexibility.
While the outer arm does most of the work (if the left leg is forwards, then the right arm is the outer arm) do focus on both shoulders when doing this exercise.
To reduce weight position the back knee on the floor. To add weight, lift the back knee.
Initially you can use the arms to lift and lower the chest while the back knee stays on the floor. The front leg takes a lot of the weight of the body off of the arms.
A nice preparation for the push up arm strengthening exercise is the half split.
Some leg flexibility and strength is required in this pose.
If you aren't that flexible then at the very least you can work at scapular stability in this pose.
With arms straight work at protracting and then relaxing your shoulder blades.
For more of a challenge with arms straight, press the floor with one hand and lift the other. If you right leg is straight then push the floor with your left hand enough that your right hand relaxes. Then lift your right hand. Remember to keep your left shoulder blade protracted as your lift your right hand.
If you can get low enough that your chest can touch the floor with elbows bent, then first protract your shoulder blades prior to using arm strength to lift your chest. Here again, if your right leg is straight try pressing strongly with the left hand and then try to relax and possibly lift your left hand.
In any of these exercises where you try to lift one hand, avoid excessive tension in the supporting arm. If it takes too much effort don't do it. The idea is to create the right amount of tension in the supporting arm so that lifting the other arm is relatively easy. This actually requires the arm, shoulder, core and legs to work together.
Another pose for strengthening the arm statically is side plank yoga pose. If your balance isn't so good then first practice balancing in side plank. You can first practice shoulder stabilization while resting on your elbow. In side plank you can try different variations to help strengthen your outer thigh, your inner thigh, your quads and even your hamstrings.
An exercise for strengthening both arms at the same time is the yoga push up. To make this arm exercise a progressive strengthening exercise lift only the chest and keep the hips on the floor. Then lift chest and hips, then lift chest, hips and knees.
As for the actual yoga push up, one way to progress in this yoga strength pose is to first practice lifting just the ribs.
The Conscious Muscle Control Pressure and Friction video includes some tips on using friction to make progressing in this exercise easier as well as strengthening the arm in different ways.
It also includes tips on how to strengthen the legs and improve flexibility in the half split pose.