We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach Caristi Type Theorems b-Metric Spaces”. also characterize the completeness of b-metric spaces with help variant contractivity condition introduced authors aforementioned article.

Very recently, by considering a self-mapping T on complete metric space satisfying general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in literature. Accordingly, inspired Proinov-type contraction conditions, Roldán López de Hierro et al. introduced novel family contractions fuzzy spaces (i...

A fully adaptive normalized nonlinear gradient descent (FANNGD) algorithm for neural adaptive filters employed for nonlinear system identification is proposed. This full adaptation is achieved using the instantaneous squared prediction error to adapt the free parameter of the NNGD algorithm. The convergence analysis of the proposed algorithm is undertaken using contractivity property of the non...

In this work, we introduce the notion of Menger probabilistic metric type space, on the other hand, we introduce a more general class of auxiliary functions in contractivity condition, following that, we obtain some multipled common fixed point theorems for a pair of mappings T : X×X · · · ×X } {{ } m-times → X and A : X→ X. As an application, we give out an example to demonstrate the validity ...

In this article, we discuss ergodicity properties of a diffusion process given through an Itô stochastic differential equation. We identify conditions on the drift and coefficients which result in sub-geometric corresponding semigroup with respect to total variation distance. also prove contractivity under class Wasserstein distances. Finally, two classes Markov processes jumps.

We extend results proven by the second author ([Oh]) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spacesX with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X),W2) satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obt...

In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures. This allows many multistep methods of practical interest to be included in the theory. In a related manner, we also con...