In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

Many existence problems in economics – for example existence of competitive equilibrium in general equilibrium theory, existence of Nash in equilibrium in game theory – can be formulated as fixed point problems. Because of this, theorems giving sufficient conditions for existence of fixed points have played an important role in economics. My treatment is schematic, focusing on only a few repres...

‎‎‎Recently Samet et al. introduced the notion of $alpha$-$psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $alpha$-$(psi,varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application...

The aim of this paper is to  establish some fixed point theorems for $alpha$-admissible Mizoguchi-Takahashi contractive mappings defined on a ${b}$-metric space which generalize the results of Gordji and Ramezani cite{Roshan6}. As a result, we obtain some coupled fixed point theorems which generalize the results of '{C}iri'{c} {et al.} cite{Ciric3}. We also present  an application in order to i...

In this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results.