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The Class of \((\alpha ,\psi )\)-Contractions and Related Fixed Point Theorems

  • Praveen Agarwal
  • Mohamed Jleli
  • Bessem Samet
Chapter

Abstract

The class of \((\alpha ,\psi )\)-contractions was introduced by Samet et al. [26]. In this chapter, we prove three fixed point theorems for this class of mappings. The presented results are extensions of those obtained in [26]. Moreover, we show that the class of \((\alpha ,\psi )\)-contractions includes as special cases several types of contraction-type mappings, whose fixed points can be obtained by means of Picard iteration. As an application, the existence and uniqueness of solutions to a certain class of quadratic integral equations is discussed. The main references of this chapter are the papers [24, 26].

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsAnand International College of EngineeringJaipurIndia
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia

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