Journal•ISSN: 1660-5446

# Mediterranean Journal of Mathematics

University of Bari

About: Mediterranean Journal of Mathematics is an academic journal published by University of Bari. The journal publishes majorly in the area(s): Mathematics & Banach space. It has an ISSN identifier of 1660-5446. Over the lifetime, 2539 publications have been published receiving 16606 citations. The journal is also known as: MedJM.

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TL;DR: In this paper, it was shown that the functions Θ(Θ(x) = [Gamma (x + 1)]^{1/x} (1 + 1/x)^x /x) and Θ (Θ (x, Θ) = Θ((Θ + 1)/x)) are Stieltjes transforms.

Abstract: We prove that the functions \(\Phi (x) = [\Gamma (x + 1)]^{1/x} (1 + 1/x)^x /x\) and \(\log \Phi (x)\) are Stieltjes transforms.

164 citations

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TL;DR: In this paper, the concept of partial b-metric spaces is introduced as a generalization of partial metric and b-measure spaces, and an analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces.

Abstract: The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.

148 citations

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TL;DR: In this article, a generalization of extending (CS) modules by using the concept of τ-large submodule was introduced, and the authors give some properties of this class of modules and study their relationship with τ-closed, τ-complement submodules and the other generalisation of extending modules (τ-complemented and τ-CS, s−τ-CS modules).

Abstract: Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of τ-large submodule which was defined in [9]. We give some properties of this class of modules and study their relationship with the familiar concepts of τ-closed, τ-complement submodules and the other generalization of extending modules (τ-complemented, τ-CS, s−τ-CS modules). We are also interested in determining when a τ-divisible module is τ-extending. For a τ-extending module M with C3, we obtain a decomposition theorem that there is a submodule K of M such that \(M = \tau (M)\,\oplus\,K\) and K is τ (M)-injective. We also treat when a direct sum of τ-extending modules is τ-extending.

134 citations

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TL;DR: In this paper, the authors present several classes of conjunctors, i.e., binary operations on [0, 1] that are used to extend the boolean conjunction from { 0, 1} to [0, 1], and characterize their respective residual implicators.

Abstract: In many practical applications of fuzzy logic it seems clear that one needs more flexibility in the choice of the conjunction: in particular, the associativity and the commutativity of a conjunction may be removed. Motivated by these considerations, we present several classes of conjunctors, i.e. binary operations on [0, 1] that are used to extend the boolean conjunction from {0, 1} to [0, 1], and characterize their respective residual implicators. We establish hence a one-to-one correspondence between construction methods for conjunctors and construction methods for residual implicators. Moreover, we introduce some construction methods directly in the class of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors.

132 citations

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TL;DR: Using Orlicz-Sobolev spaces and a variant of the Mountain Pass Lemma of Ambrosetti-Rabinowitz, the authors obtained existence of a (positive) solution to a semilinear system of elliptic equations.

Abstract: Using Orlicz-Sobolev spaces and a variant of the Mountain-Pass Lemma of Ambrosetti-Rabinowitz we obtain existence of a (positive) solution to a semilinear system of elliptic equations. The admissible nonlinearities are such that the system is superlinear and subcritical. The Orlicz setting used here allows us to consider nonlinearities which are not (asymptotically) pure powers. Moreover, by an interpolation theorem of Boyd we find an elliptic regularity result in Orlicz-Sobolev spaces. A bootstrapping argument implies that the above mentioned solutions are classical.

109 citations