Some results on weakly inward mapping in geodesic metric spaces

Geodesic spaces are convex nonlinear spaces. Convexity is a significant tool to generalize some properties of Banach spaces. In this paper, the characterization of weakly inward was extended to CAT(0) spaces and give equivalent condition for the existence of fixed point for multivalued mapping

Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings

Suppose thatKis nonempty closed convex subset of a uniformly convex and smooth Banach spaceEwithPas a sunny nonexpansive retraction andF:=F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠∅. LetT1,T2:K→Ebe two weakly inward nonself asymptotically nonexpansive mappings with respect toPwith two sequences{kn(i)}⊂[1,∞)satisfying∑n=1∞(kn(i)-1)<∞(i=1,2), respectively. For any givenx1∈K, suppose that{xn}is a sequence generated iteratively byxn+1=(1-αn)(PT1)nyn+αn(PT2)nyn,yn=(1-βn)xn+βn(PT1)nxn,n∈N, where{αn}and{βn}are sequences in[a,1-a]for somea∈(0,1). Under some suitable conditions, the strong and weak convergence theorems of{xn}to a common fixed point ofT1andT2are obtained.

FIXED POINT THEORY FOR VARIOUS CLASSES OF INWARD MULTIVALUED MAPS

In this paper we present new fixed point theorems for inward and weakly inward type maps between Fréchet spaces. We also discuss Kakutani–Mönch and contractive type maps.