New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality Faà di Bruno’s formula for higher order derivatives the composition.

In this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers. c © 2007 Elsevier Ltd. All rights reserved.

Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions.

The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contr...

We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We als...

The study of integer representations as a sum powers is still very long standing problem. In this work, the representation cube introduced and investigated for non-zero distinct solution. Let \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\) d be any positive integers such that - \(a_n\)-1= \(a_n\)-1 \(a_n\)-2 = \(a_2\) \(a_1\) d. This formulates some general results sums n cube. particular, research in...