In this paper, we consider a nonlinear viscoelastic Kirchhoff equation with the presence of both distributed delay term, Balakrishnan‐Taylor damping, and logarithmic nonlinearity. We describe a exponential decay of solutions, and we obtained the asymptotic stability result of the global solution. This study is a continuation of Boulaaras's works (Math. Meth. Appl. Sci. 2019;42:4795– 4814 and Alex. Eng. J. 2020;59:1059–1071)

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Abstract. In this paper, we introduce the notion of subsequential continuity for a hybrid pair of maps and combine this concept with compatibility, to establish a coincidence and common fixed point theorem for a hybrid quadruple of maps. Our main result also demonstrates that several fixed point theorems can be unified using implicit relations. We also give two examples in support our results.

In this paper we define the tangential property in partial metric spaces and metric-like spaces to prove some common fixed point theorems for two pairs of generalized weakly contractions, some examples are given to illustrate ours results.

The aim of this paper is to prove common fixed point theorems for multivalued contraction of Wordowski type, by using the concept of subsequential continuity in the setting of set valued context contractions with compatibility. We have also given an example and an application to integral inclusions of Fredholm type to support our results.