In this paper, we study for some of the fixed point of mapping for a self map on a metric space under a contractive of integral type.

In this paper, we investigate new solutions to the Rhoades' discontinuity problem on existence of a self-mapping which has fixed point but is not continuous at metric spaces. To do this, use number defined as n(x,y)=[d(x,y)]β[d(x,Ty)]α[d(x,Ty)]γ[(d(x,Ty)+d(x,Ty))/2]1−α−β−γ, where α , β γ ∈ ( 0,1 ) with + < 1 and some interpolative type contractive conditions. Also, geometric properties Fix(T...

Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to open problem CC: what is (are) condition(s) make any circle C?0,? common fixed for two (or more than two) self-mappings? To do this, modify known contractions which are used in fixed-point theorems such Hardy–Rogers-type cont...

Abstract In this article, we introduce two notions of interpolative F -contractions with shrink map and map. We also study the existence E -fixed points by using these notations on a metric space endowed binary relation. As an application consequence main results, get some other interesting results like common fixed point result, result equipped graph, theorem for solution integral equations.