Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces

Abstract

We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order (p,q)-difference equations with integral boundary value conditions.

Keywords

• Banach space
• enriched <i>φ</i>-contraction
• enriched cyclic <i>φ</i>-contraction
• fixed point
• Maia type fixed point theorem
• (<i>p</i>,<i>q</i>)-difference equation