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## Online first articles

Articles are posted here individually soon after proof is returned from authors, before the corresponding journal issue is completed. All articles are in their final form, including issue number and pagination. For a list of accepted articles, see Articles in press.

#### Vol. 62, no. 2 (2021)

 Multidimensional common fixed point theorems for multivalued mappings in dislocated metric spaces. Deepa Karichery and Shaini Pulickakunnel Motivated by the $F$-contraction introduced by Wardowski [Fixed Point Theory Appl. 2012, 2012:94], we introduce three types of multidimensional Ciric-type rational $F$-contractions for multivalued mappings in dislocated metric spaces. Using these contractions, we establish fixed points of $N$-order for multivalued mappings. Our result generalizes the main result obtained by Rasham et al. [J. Fixed Point Theory Appl. 20 (2018), no. 1, Paper no. 45]. 275–293 Split exact sequences of finite MTL-chains. J. L. Castiglioni and W. J. Zuluaga Botero This paper is devoted to presenting ordinal sums of MTL-chains as a particular case of split short exact sequences of finite chains in the category of semihoops. This module theoretical approach will allows us to prove, in a very elementary way, that every finite locally unital MTL-chain can be decomposed as an ordinal sum of archimedean MTL-chains. Furthermore, we propose the study of MTL-chain extensions and we show that ordinal sums of locally unital MTL-chains are a particular case of these. 295–304 A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces. Kazeem Olalekan Aremu, Chinedu Izuchukwu, Olawale Kazeem Oyewole, and Oluwatosin Temitope Mewomo We propose a modified Halpern-type algorithm involving a Lipschitz hemicontractive non-self mapping and the resolvent of a convex function in a Hadamard space. We obtain a strong convergence of the proposed algorithm to a minimizer of a convex function which is also a fixed point of a Lipschitz hemicontractive non-self mapping. Furthermore, we give a numerical example to illustrate and support our method. Our proposed method improves and extends some recent works in the literature. 305–325 A Ricci-type flow on globally null manifolds and its gradient estimates. Mohamed H. A. Hamed, Fortuné Massamba, and Samuel Ssekajja Locally, a screen integrable globally null manifold $M$ splits through a Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$ tangent to its radical distribution. The leaf $M'$ carries a lot of geometric information about $M$ and, in fact, forms a basis for the study of expanding and non-expanding horizons in black hole theory. In the present paper, we introduce a degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor of $M$. Several new gradient estimates regarding the flow are proved. 327–349 Complete lifting of double-linear semi-basic tangent valued forms to Weil like functors on double vector bundles. Włodzimierz M. Mikulski Let $F$ be a product preserving gauge bundle functor on double vector bundles. We introduce the complete lifting $\mathcal{F}\varphi:FK\to \wedge^p T^*FM\otimes TFK$ of a double-linear semi-basic tangent valued $p$-form $\varphi:K\to \wedge^p T^*M\otimes TK$ on a double vector bundle $K$ with base $M$. We prove that this complete lifting preserves the Frolicher–Nijenhuis bracket. We apply the results obtained to double-linear connections. 351–363