Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

In this paper, we introduce the notion of complex valued G-metric spaces and prove contraction principle in the newly spaces. Mathematics Subject Classification: 47H10, 54H25

In this paper, we prove some approximate fixed point results for proximinal valued $beta$-contractive multifunctions on metric spaces. We show that our results generalize some old fixed point results in the literature.

In this paper, we introduce complex valued rectangular b-metric spaces. We prove an analogue of Banach contraction principle. We also prove a different contraction principle with a new condition and a fixed point theorem in this space. Finally, we give an application of Banach contraction principle to linear equations. c ©2015 All rights reserved.