Let (X, d) be a pointed compact metric space, let 0 < α < 1, and let φ : X → X be a base point preserving Lipschitz map. We prove that the essential norm of the composition operator Cφ induced by the symbol φ on the spaces lip0(X, d α) and Lip0(X, d α) is given by the formula ‖Cφ‖e = lim t→0 sup 0<d(x,y)<t d(φ(x), φ(y))α d(x, y)α whenever the dual space lip0(X, d α)∗ has the approximation prope...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

in this paper, the notion of $psi -$weak contraction cite{rhoades} isextended to fuzzy metric spaces. the existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. our resultgeneralizes a result of gregori and sapena cite{gregori}.

‎In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath  might be called their  definitive versions. Also, we show that there are examples which show that our main theorems are  genuine generalizations of Theorem 3.1 and 3.2 of [M.A. Miandaragh, M. Postolache and S. Rezapour,  {it Approximate fixed points of generalized convex contractions}, Fixed Poi...

This paper studies a general p-contractive condition of self-mapping T on X, where X ,d is either metric space or dislocated space, which combines the contribution to upper-bound dTx , Ty, x and y are arbitrary elements in weighted combination distances dx,y dx,Tx,dy,Ty,dx,Ty,dy,Tx, dx,Tx−dy,Ty dx,Ty−dy,Tx. The asymptotic regularity convergence Cauchy sequences unique fixed point also discussed...

We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].

In this paper, we obtain the metric of space-time generated by a charged and rotating gravitational body surrounded loud strings, namely, Kerr–Newman black hole with addition cloud strings. background, find radial solutions Dirac equation for massive particles show that they are given in terms Generalized Heun functions. The dependence these on parameter codifies presence strings is pointed out.