Common Fixed Point Theorems and $Q$-Property for Quasi-Contractive Mappings under $c$-Distance on TVS-Valued Cone Metric Spaces Without the Normality

Abstract

Fixed point and common fixed point results for mappings satisfying quasi-contractive conditions expressed in the terms of $c$-distance on TVS-valued cone metric spaces (without the underlying cone which is not normal) are obtained, and $P$-property and $Q$-property for mappings in the terms of $c$-distance are discussed. Our results generalize and improve many known results.