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Till now, there exists enormous literature showing existence of fixed points using expansive mappings. But the existence of common and coincidence fixed points for a sequence of functions using expansive mappings is still uncharted. In the present article, some coincidence and common fixed point results for a sequence of mappings satisfying generalized weakly expansive conditions in the setting of quasi partial metric spaces have been investigated. The effectiveness of obtained results have been verified with the help of some comparative examples.

In the present work, the concept of F -generalized contractive type mappings by using C -class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples.

In the present article, the notion of αH-ψH-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa's (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has been presented as an application.