Question

Mathematical relation between ionization enthalpy,electron gain enthalpy and electron affinity

Answer 1

ionization energy is the energy required to remove electron from isolated gaseous atom. ions are formed as a result of ionization energy, hence named. but in case of F- removing an electron forms a neutral atom. 
electron affinity( more appropriatly electron gain enthalpy) is the energy released when an extra elecrtron is added to the valence shell of neutral gaseous atom. 

In the above case energy required to remove an electron from F- and energy released when an electron is added to F will be equal.

Answer 2

see when size of the cation is more then the value of i.p and e.n,e.a will decrease and the size of the anion will decreases also the values will be like the above case only