We give some new definitions of "Equation missing"<!-- image only, no MathML or LaTex -->-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete "Equation missing"<!-- image only, no MathML or LaTex -->-metric spaces. We get some improved versions of several fixed point theorems in complete "Equation missing"<!-- image only, no MathML or LaTex -->-metric spaces.

In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works.

In this work we have considered several common fixed point results in b-metric spaces for weak compatible mappings. By applications of these results we establish some fixed point theorems in b-fuzzy metric spaces.

In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.

An ingenious approach to generalize Banach contraction principle was adopted by Suzuki in his seminal papers (Proc Am Math Soc 136:1861–1869, 2008 , Nonlinear Anal Theory Methods Appl 71:5313–5317, 2009 ). In this paper we prove certain common fixed point results for generalized Suzuki contractions in the set-up of b-metric spaces, where the b-metric function is not necessarily continuous. Finally, some examples are presented to verify the effectiveness and applicability of our main results.