Fixed point theorems for generalized asymptotic pointwise -contraction mappings involving orbits in modular function spaces

In this work, we prove new fixed point theorems for generalized asymptotic pointwise ρ -contractions and strongly asymptotic pointwise ρ -contraction mappings involving orbits in modular function spaces. The results of this work extend and improve the recent results of Khamsi and Kozlowski [M.A. Khamsi, W.M. Kozlowski, On asymptotic pointwise contractions in modular function spaces, Nonlinear Analysis: Theory Methods and Applications 73 (2010) 2957–2967] and Nicolae [A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory and Applications (2009) Article ID 458265, 19 pages].