We consider the topological structure of sublinear quasi-metrics in locally convex cones and define notion a quasi-metric cone. The presence upper bounded neighborhoods, gives necessary sufficient conditions for quasi-metrizability cones. In particular, we investigate boundedness separatedness characterize metrizability

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some...

Correspondence: lhorvath@almos. vein.hu Department of Mathematics, University of Pannonia, 8200 Veszprém, Egyetem u. 10., Hungary Abstract In this paper, a new parameter-dependent refinement of the discrete Jensen’s inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem w...

We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.

We study continuity properties of law-invariant (quasi-)convex functions f : L∞( ,F,P) → (−∞,∞] over a non-atomic probability space ( ,F,P). This is a supplementary note to Jouini et al. (Adv Math Econ 9:49–71, 2006).

In this paper, we define and study convergence of an Ishikawa type iteration scheme with a new and weaker control condition for two nonself asymptotically quasi-nonexpansive mappings on a uniformly convex Banach space.

Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...