Fixed point results for Gm-Meir-Keeler contractive and G-(α,ψ)-Meir-Keeler contractive mappings

Fixed Point Theorems with Applications to the Solvability of Operator Equations and Inclusions on Function Spaces

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 2Department of Mathematical Analysis, University of Valencia, Spain 3Centre Universitaire Polydisciplinaire, Kelaa des Sraghna, Morocco 4Universite Cadi Ayyad, Laboratoire de Mathematiques et de Dynamique de Populations, Marrakech, Morocco 5Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy

Some fixed point theorems for generalized contractive mappings in complete metric spaces

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.

Fixed point results for α-implicit contractions with application to integral equations

Recently, Aydi et al. [On fixed point results for α-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21(1):40–56, 2016] proved some fixed point results involving α-implicit contractive conditions in quasi-b-metric spaces. In this paper we extend and improve these results and derive some new fixed point theorems for implicit contractions in ordered quasi-b-metric spaces. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.