Search

The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler's theorem by using weak partial Hausdorff b-metric spaces in the context of a weak partial b-metric space. We present a non-trivial example which show the validity of our result and an application to nonlinear Volterra integral inclusion for the applicability purpose. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i ∗ γ (X) A i and give a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical convergence, which is a recently introduced summability method. The names of our new methods are A I -lacunary statistical convergence and strongly A I -lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted by S θ A I , F and N θ A I , F , respectively. We give some inclusion relations between S A I , F , S θ A I , F and N θ A I , F . We also investigate Cesáro summability for A I and we obtain some basic results between A I -Cesáro summability, strongly A I -Cesáro summability and the spaces mentioned above. [ABSTRACT FROM AUTHOR]