STUDY ON EXISTENCE THEORY FOR INTEGRAL EQUATIONS OF MIXED TYPE

GHASEM ALIZADEH  AFROUZI; SOHRABALI  YOUSEFI; R.A.  TALARPOSHTI

STUDY ON EXISTENCE THEORY FOR INTEGRAL EQUATIONS OF MIXED TYPE

Authors

GHASEM ALIZADEH AFROUZI Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
SOHRABALI YOUSEFI Department of Mathematics, Shahid Beheshti University , Tehran, Iran
R.A. TALARPOSHTI Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Keywords:

Measure of weak noncompactness, Nonlinear mixed integral equation, Darbo’s theorem, Banach algebra

Abstract

This article presents an existence of monotonic solution for the nonlinear mixed Volterra-Fredholm integral equation acting on $L_1[0, 1]$. By using the techniques of the De Blasi measure of weak noncompactness, we employ the basic fixed point theorems such as Darbo s theorem to obtain the mentioned aims in Banach spaces.