Example.jsx

import React from 'react';
import Picture from './Picture';

export const PictureWrapper = () => {
  return (
    <div>
      <Picture
        src="http://placekitten.com/g/300/300"
        srcSet="https://placeimg.com/440/440/nature 440w, https://placeimg.com/640/640/nature 640w"
        sizes="(max-width: 500px) 440w, 640w"
      />
    </div>
  );
};

Picture.jsx

import * as React from 'react';
import createClass from 'create-react-class';
import PropTypes from 'prop-types';

const Picture = createClass({
  displayName: 'Picture',

  getInitialState() {
    const { srcSet, sizes } = this.props;

    return {
      srcSet,
      sizes
    };
  },

  handleError() {
    this.setState({
      srcSet: null,
      sizes: null
    });
  },

  render() {
    const { srcSet, sizes } = this.state;
    const { src, style } = this.props;

    return (
      <div style={style}>
        <img
          src={src}
          srcSet={srcSet}
          sizes={sizes}
          style={style}
          onError={this.handleError}
        />
      </div>
    );
  }
});

Picture.propTypes = {
  src: PropTypes.string.isRequired,
  srcSet: PropTypes.string,
  sizes: PropTypes.string,
  style: PropTypes.object
};

export default Picture;