In this paper, we will present some fixed point results for two classes of generalized contractions of Boyd-Wong type in partial b-metric spaces. More precisely, the structure of the paper is the following. In section one, we present some useful notions and results. The aim of section two is to introduce the concepts of Boyd-Wong F-contractions of type A and of type B and establish some new common fixed point results in partial b-metric spaces. We show the validity and superiority of our main results by suitable examples which are visualized by corresponding surfaces and related graphs. In section three, we correct some slip-ups in some recent papers. Finally, in section four, two applications to integral equation and periodic boundary value problem are included which make effective the new concepts and results.
This paper attempts to study some geometric properties along with the existence of a generalized weakly Ricci symmetric manifold and find out the reduced form of defining conditions of such a manifold. It is observed that every generalized weakly Ricci symmetric manifold is an almost generalized pseudo-Ricci symmetric manifold. We also find out the conditions for which a weakly Ricci symmetric manifold becomes a Ricci pseudosymmetric manifold in the sense of Deszcz.
Abstract. The main objective of the paper is to provide a full classification of quasiconformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.
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