Fixed Point Results in Controlled Metric Spaces with Applications

The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations

Generalized Theta-contractive fuzzy mappings

Altun, Ishak/0000-0002-7967-0554;WOS: 000443287900059The aim of this paper is to obtain some common alpha-fuzzy fixed point theorems under generalized Theta-contraction in the setting of complete metric space. In this way, we generalize various results of literature including the main result of Hancer et al. (Fixed Point Theory, 18 (2017), 229-236). We also provide an example to show the significance of the results investigated in this paper.Deanship of Scientific Research (DSR), University of Jeddah, Jeddah; DSR, UOJThis article was funded by the Deanship of Scientific Research (DSR), University of Jeddah, Jeddah. Therefore, authors acknowledges with thanks DSR, UOJ for financial support

Banach Contraction Principle-Type Results for Some Enriched Mappings in Modular Function Spaces

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched ρ-contractions and enriched ρ-Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched ρ-contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched ρ-contractions. We make a first ever attempt to prove existence results for enriched ρ-Kannan mappings and deduce the result for ρ-Kannan mappings. Note that even ρ-Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples