This study presents a wide-field near-infrared ( K-band ) survey in two fields ; SA 68 and Lynx 2 .
The survey covers an area of 0.6 deg . ^ { 2 } , complete to K=16.5 .
A total of 867 galaxies are detected in this survey of which 175 have available redshifts .
The near-infrared number counts to K=16.5 mag .
are estimated from the complete photometric survey and are found to be in close agreement with other available studies .
The sample is corrected for incompleteness in redshift space , using selection function in the form of a Fermi-Dirac distribution .
This is then used to estimate the local near-infrared luminosity function of galaxies .
A Schechter fit to the infrared data gives : M ^ { \ast } _ { K } = -25.1 \pm 0.3 , \alpha = -1.3 \pm 0.2 and \phi ^ { \ast } = ( 1.5 \pm 0.5 ) \times 10 ^ { -3 } Mpc ^ { -3 } ( for H _ { 0 } = 50 Km/sec/Mpc and q _ { 0 } = 0.5 ) .
When reduced to \alpha = -1 , this agrees with other available estimates of the local IRLF .
We find a steeper slope for the faint-end of the infrared luminosity function when compared to previous studies .
This is interpreted as due to the presence of a population of faint but evolved ( metal rich ) galaxies in the local Universe .
However , it is not from the same population as the faint blue galaxies found in the optical surveys .
The characteristic magnitude ( M ^ { \ast } _ { K } ) of the local IRLF indicates that the bright red galaxies ( M _ { K } \sim - 27 mag . )
have a space density of \leq 5 \times 10 ^ { -5 } Mpc ^ { -3 } and hence , are not likely to be local objects .