Fixed points for generalized "Equation missing"-contractions on generalized metric spaces

Abstract

Abstract In this paper, we introduce some generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>ψ</mml:mi><mml:mo>)</mml:mo></mml:math> -contractive mappings in the setting of generalized metric spaces and, based on the very recent paper (Kirk and Shahzad in Fixed Point Theory Appl. 2013:129, 2013), we omit the Hausdorff hypothesis to prove some fixed point results involving such mappings. Some consequences on existing fixed point theorems are also derived. MSC: 46T99, 47H10, 54H25.