On the existence of solutions of non-linear 2D Volterra integral equations in a Banach Space


Chauhan H. V. S. , Singh B., Tunç C. , Tunç O.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.116, no.3, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 116 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s13398-022-01246-0
  • Title of Journal : REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Keywords: Integral equations, Measure of non-compactness (MNC), Petryshyn fixed point theorem (PFPT), SOLVABILITY, BOUNDEDNESS

Abstract

In this work, we examine the solvability of non-linear 2D Volterra integral equations through Petryshyn fixed point theorem in Banach space C([0, c] x [0, d]). Our work covers many previous results that occur in non-linear analysis and some real-world problems under some weaker conditions. The efficiency of our work is presented by some examples.