Mathematical Science Letters An International Journal

Common fixed point for generalized weak contractions in metric spaces and application to nonlinear integral equation

Solvability of infinite systems of second-order differential equations with boundary conditions in ℓp

In this paper, governed by the fundamental solutions we introduce the Green's function of the second-order differential equations in general form with respect to boundary conditions and deal with the solvability of the innite system of second-order differential equations with p, q ∈ C([0, T ], ℝ) and the boundary conditions  i (0) = u i (T ) = 0. We remark that the subjected system has not been previously considered and this investigation complements several results in the literature. Using the ideas of Hausdorff measure of noncompactness and Meir-Keleer condensing operator we seek the sufficient conditions to justify the existence of solutions for the aforementioned system in Banach sequence space ℓ p (1 ≤ p < ∞). Finally, an example is given to ascertain the efficiency of the results. Mathematics Subject Classication (2010): 47H10, 34A34, 34B27, 35E05

On the PC PC\mathcal{PC}-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

Abstract In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of S $\mathcal{S}$-asymptotically ω-periodic mild solutions. The applied techniques are supported by the concept of measure of noncompactness in conjunction with the well-known Darbo–Sadovskii and Tichonov fixed-point theorems. Furthermore, an example to the fractional initial/boundary value Cauchy problem is concerned to illustrate our main results

Further Remarks on N-Distance-Balanced Graphs

Throughout this paper, we present a new strong property of graph so-called nicely n-distance-balanced which is notably stronger than the concept of n-distance-balanced recently given by the authors. We also initially introduce a newgraph invariant which modies Szeged index and is suitable to study n-distance-balanced graphs. Looking for the graphs extremal with respect to the modiedSzeged index it turns out the n-distance-balanced graphs with odd integer n arethe only bipartite graphs which can maximize the modied Szeged index and thisalso disproves a conjecture proposed by Khalifeh et al. [Khalifeh M.H.,Youse-Azari H., Ashra A.R., Wagner S.G.: Some new results on distance-based graphinvariants, European J. Combin. 30 (2009) 1149-1163]. Furthermore, we gathersome facts concerning with the nicely n-distance-balanced graphs generated by somewell-known graph products. To enlighten the reader some examples are provided.Moreover, a conjecture and a problem are presented within the results of this article