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This paper deals with new results on Gruss inequality by using recent fractional integral operators. In fact, based on the (k, s, h) -- Riemann-Liouville and the (k, h) --Hadamard fractional operators, we establish several integral results. For our results, some very recent results on the paper: [A Gruss type inequality for two weighted functions. J. Math. Computer Sci., 2018.] can be deduced as some special cases. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of F--G--contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F--metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results. [ABSTRACT FROM AUTHOR]

Let f be a transcendental entire function defined in the open complex plane ℂ. A difference-monomial generated by f is an expression of the form F = fn(fm -1) ... (f (z+cj))..., where n, m and Vj are all non-negative integers. Now for the sake of definiteness let us take, Mi[f ] = fn(fm -1) ... (f (z+cj))..., where 1 ≤ i ≤ d. If M1 [f], M1 [f ],..., Mn [f] are such monomials in f as defined above, then ψ[f] = a1M1[f] + a2M2[f] + ... + anMn [f] where ai ≠ 0 (i = 1, 2,..., n) is called a difference-polynomial generated by f. In this paper, we compare the Valiron defect with the relative Nevan-linna defect of a particular type of differential-difference polynomial generated by a transcendental entire function with respect to integrated moduli of logarithmic derivative. Some examples are provided in order to justify the results obtained. [ABSTRACT FROM AUTHOR]

Let G be a graph with n vertices and m edges. The minimum edge dominating energy is defined as the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of the graph G. In this paper, some lower and upper bounds for the minimum edge dominating energy of graph G are established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a weak MT-cyclic Reich type contractions and obtain the existence theorems for best proximity point for self-mappings defined on the complete metric spaces. Our results improve and generalize some results in literature. Also, we give some applications of our results to solving some classes of non-linear integral and differential equations. [ABSTRACT FROM AUTHOR]

This work is concerned with the initial boundary value problem for a nonlinear viscoelastic Petrovsky wave equation utt + Δ²u - ... g(t - τ) Δ²u(τ)dτ - Δut - Δutt + ut |ut|m-1 = u|u|p-1. Under suitable conditions on the relaxation function g, the global existence of solutions is obtained without any relation between m and p. The uniform decay of solutions is proved by adapting the perturbed energy method. For p > m and sufficient conditions on g, an unboundedness result of solutions is also obtained. [ABSTRACT FROM AUTHOR]