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In the current paper, we discuss sufficient and necessary conditions for the existence of best proximity points for cyclic f- contractive mappings in the setting of strictly convex Banach spaces. Extensions of Edelstein's theorem are considered as well as an extension of a main result in Park [Park, S. (1978). Fixed points of f-contractive maps. Rocky Mountain J. Math. 8:743–750]. Another existence result of best proximity points will be obtained for asymptotically relatively nonexpansive mappings under different conditions with respect to the recent paper of Rajesh and Veeramani [Rajesh, S., Veeramani, P. (2016). Best Proximity point theorems for asymptotically relatively nonexpansive mappings. Numer. Funct. Anal. Optim. 37:80–91]. [ABSTRACT FROM AUTHOR]

Assume that X, Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f: X → Y is a standard coarse isometry. In this paper, we show that if then there is a linear isometry U : X → Y so that where is defined by Representation properties of coarse isometries in free ultrafilter limits on are also discussed. [ABSTRACT FROM AUTHOR]

We obtain a new class of compact Hausdorff spaces K for which c 0 can be nontrivially twisted with C ( K ) . [ABSTRACT FROM AUTHOR]

In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr's common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces. [ABSTRACT FROM AUTHOR]

It is shown that if an N-function φ is submultiplicative, then its conjugate function φ* cannot be submultiplicative. Moreover, we have the following characterization of power functions among N-functions: if an N-function φ is C-submultiplicative and its conjugate function φ* is C-submultiplicative for some C, C > 0, then φ is equivalent to a power function. [ABSTRACT FROM AUTHOR]

In this note we introduce a new 2-dimensional parameter, we also discuss a related characterization of Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this article, we study the structure of minimal sets of relatively non-expansive mappings. We consider the cyclic and the noncyclic cases and show that results alike to the celebrated Goebel-Karlovitz lemma for non-expansive self-mappings can be obtained for relatively non-expansive mappings. [ABSTRACT FROM AUTHOR]