In this paper, we initiate the notion of generalized multivalued ( α K * , Υ , Λ ) -contractions and provide some new common fixed point results in the class of α K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

In this paper, we initiate the notion of Ćirić type rational graphic Υ , Λ -contraction pair mappings and provide some new related common fixed point results on partial b-metric spaces endowed with a directed graph G. We also give examples to illustrate our main results. Moreover, we present some applications on electric circuit equations and fractional differential equations.

The purpose of this paper is to generalize fixed point theorems introduced by Jleli et al. (J. Inequal. Appl. 2014:38, 2014) by using the concept of triangular α-orbital admissible mappings established in Popescu (Fixed Point Theory Appl. 2014:190, 2014. Some examples are given here to illustrate the usability of the obtained results. MSC: 46S40; 47H10; 54H25