Some surjectivity theorems with applications

H. K. Pathak and S. N. Mishra

School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur 492010, India
Corresponding author S. N. Mishra Department of Mathematics, Walter Sisulu University, Mthatha 5117, South Africa


Abstract: In this paper a new class of mappings, known as locally $\lambda $-strongly $\phi $-accretive mappings, where $\lambda $ and $\phi $ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly $\phi $-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally $\lambda $-strongly $\phi $-accretive mappings by using Caristi-Kirk fixed point theorem. In the sequel, we introduce the notion of generalized directional contractor and prove a surjectivity theorem which is used to solve certain functional equations in Banach spaces.

AMSclassification: primary 47H15; secondary 47H05.

Keywords: strongly \phi -accretive, locally strongly \phi -accretive, locally \lambda -strongly \phi -accretive, fixed point theorem.

DOI: 10.5817/AM2013-1-17