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Abstract: In this article, we will show that (1) the results about the triple I method for fuzzy reasoning obtained in the paper “Computers and Mathematics with Applications 44 (2002) 1567–1579” are correct; (2) Example 2.1 in the paper “Notes on triple I method of fuzzy reasoning” presented by Hua-wen Liu is incorrect; (3) -triple I method presented by Liu is a generalization of -triple I method. [Copyright &y& Elsevier]

Abstract: In this paper, we define generalized -Horadam sequence . After that, we study the properties of the generalized -Horadam sequence and prove some of these properties by means of determinant. Also, we obtain a generating function for the generalized -Horadam sequence. [Copyright &y& Elsevier]

Abstract: The main object of the present paper is to discuss some extensions of certain integral operators and to obtain their order of convexity. Several other closely related results are also considered. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some Tauberian theorems for the Abel summability method in terms of regularly generated sequences which generalizes some results obtained in Çanak and Totur [İ. Çanak, Ü. Totur, A note on Tauberian theorems for regularly generated sequences, Tamkang J. Math. 39 (2) (2008) 187–191]. [Copyright &y& Elsevier]

Abstract: In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation with -periodic coefficients, where , . Also, we obtain that the generalized solution is periodic with -period. [Copyright &y& Elsevier]

Abstract: In this paper we establish some new generalizations and refinements of Hölder’s inequality and some related inequalities. We also show that many existing inequalities related to the Hölder inequality are special cases of the inequalities presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish some new generalizations of Aczél’s inequality and of Bellman’s inequality; we will conclude by presenting some refinements of these inequalities. [Copyright &y& Elsevier]