onclick function is not working in react native application

You need to use one of the following wrapper components. Below are just the ones listed, which are available cross-platform.

TouchableHighlight

<TouchableHighlight onPress={this.openPopup}>
    <View>...</View>
</TouchableHighlight>

TouchableOpacity

<TouchableOpacity onPress={this.openPopup}>
    <View>...</View>
</TouchableOpacity>

TouchableWithoutFeedback

<TouchableWithoutFeedback onPress={this.openPopup}>
    <View>...</View>
</TouchableWithoutFeedback>

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Note the above are on their way to being deprecated. Check out Pressable

Try this-

<TouchableOpacity onPress={this.openPopup}> 
    <View> <Text>...</Text> </View> 
</TouchableOpacity>